I want to talk specifically about the so called "Apostolic Fathers" these are often considered distinct from the other Church Fathers, they were supposedly the direct successors of The Apostles, the 2nd, 3rds and 4th of the various Bishoprics.
Their period is sometimes arbitrarily dated as ending in 125 AD.
There should be at least 20 (each of the 12 plus Paul, plus the half siblings of Jesus, plus Joseph of Arimathea and Nicdemus and Lazurus, and Cleopas, at the very least all held Apostolic rank, and that is with me reluctantly conceding to those who would deny the rank to the Female Eyewitnesses of the Resurrection) individuals to hold such a rank, but really a lot more since they each brought The Gospel to many cities, and founded many churches, and it can be shown Biblical church government was not originally monarchical. There is also the 70 Disciples to consider. There were actually 100s of people in the upper room at Pentacost.
But only a handful are preserved as having written or said anything for us to quote. Since history is written by the winners, and it was the scribes of the Catholic and Eastern Orthodox traditions who decided what works to preserve, it's safe to assume that they were very selective. Some of those other supposed successors we have traditions about, but not writings or sermons they preached.
Most of that handful we have are from being quoted by later Church Fathers. It's Clement of Rome and Ignatius alone who left significant writings behind that we still have, and of the many works attributed to Clement only First Clement (aka The Epistle of Clement to The Corinthians) is genuine. And it's valid to question if those writings were even preserved accurately. God promised to preserve his Word, not anything ever written by a Christian.
Other works affiliated with this era are unnamed authors like Shepherd of Hermas or the Didachae (which I glibly call the first Baptist Constitution). The Didachae is often considered the oldest extra Biblical Christian writing. It has nothing majorly objectionable, but does add to Scripture like saying you need to fast for a day before Baptism. It doesn't seem to address Faith Alone or Eternal Security either way.
Of all the supposed Apostolic Fathers who left writings behind. Only Clement of Rome is identified by tradition with a person named in the NT, the Clement Paul mentioned in Philippians. Contrary to how Catholics try to twist it First Clement definitely teaches Salvation by Faith Alone, but doesn't address Eternal Security one way or the other. But he's a problem because the whole motive behind the letter was thinking he had authority to tell the Corinthians what to do, the root of Papal authority was kind of there already.
Yet when he refers to Peter only once in the Epistle, he is very vague, and does not say where he was when he died or confirm him having been to Rome at all, or claim to be a successor of Peter or to have been appointed by Peter as Tertullian claimed Clement was. He talks about Paul far more but doesn't confirm he was a student or associate directly of him either.
He also never mentioned Philipi or the Philippians. So is this really the same Clement? It was a not uncommon Roman name (Philipi was a city where everyone had Roman Citizenship). Later Clementine traditions would seek to say he was Titus Flavius Clemens, a member of the Flavian family. There is reason to suspect Titus Clemens might have become a Christian, but given his age and biography no way he was ever in Philipi, or prominent at all while Paul was alive.
Many Protestant and Evangelical Christians have grown accustomed to accepting the Catholic Tradition linking Peter to Rome. Often arguing based on Irenaeus and the Apostolic Constitutions that it was Paul not Peter who appointed Linus to be Bishop of the Roman church. But still believing Peter had been there. I myself in the past had accepted it, saying based on Eusebius that Peter had came to Rome twice, in 42 AD and later in the 60s when he died.
Sometimes extra-Biblical traditions can seem universal but still be false. Like the whole Nimrod masterminded Babel thing.
The oldest source on Peter in Rome is really the apocryphal Ascension of Isaiah, but that doesn't even name the one of the 12 it says Nero Martyrded. The author could have considered Nero responsible simply for it being done by the Roman government, even if there was no direct personal involvement from Nero. Andrew was traditionally held to be martyred in Achaia Greece, the city of Patrae in the northern Peloponnese, by the order of the Roman Governor. Traditional date is November 30th 60 AD.
But also maybe the assumption that the Ascension of Isaiah was identifying Nero is wrong. It never says anything about Rome, the main identifier with Nero besides supposedly killing one of the 12 is having killed his mother. But certainly others throughout history have killed their mothers. The Ascension of Isaiah is the product of a time when the trendy thing was to identify The Antichrist (who this killer of one of the 12 is supposed to be) as a Jewish False Messiah. Also if the author wanted readers to think of Nero and Agrippina, the incest angle would have been much better to lead with.
The only one of the 12 who's martyrdom is documented in Scripture was James the Son of Zebedde. He was killed by Herod Agrippa, there are reasons in Acts 12 to see Agrippa as a type of The Antichrist, especially if you have Ezekiel 28 in mind.
Agrippa's mother was Berenice, the daughter of Herod The Great's sister Salome. We don't know what happened to her, she's last mentioned retiring to Rome well before her son becomes King. Our main source on Agrippa's life is Jospehus who was a friend of his son Agirppa II and tended to portray Agrippa very positively. If he had for some reason murdered his mother Josephus would have concealed it. In the 2nd century other sources on the 1st century AD were around that haven't survived, like the other 3 of Philo's 5 books about Jewish persecutors contemporary with Caligula, and Justus who had an antagonist relationship with Josephus and Agrippa II.
I don't want to accuse Agrippa of anything, but it's highly possible a critic of the Agrippas like Justus could have slandered them. And then that slander influenced the author of the Ascension of Isaiah.
But it could also simply be that the author meant something allegorical rather then literal with "Slayer of his Mother", like being a slayer of his own people. If he had Gnostic heresies in mind (for or against them) he could have been thinking of the relationship between Sophia and the Ialdobath in Gnostic cosmologies. It also certainly could be he meant this to allude to The Beast killing the Whore of Babylon in Revelation 17.
How did The Gospel come to Rome?
From The Bible, we know in Acts 2 some Jews who lived in Rome were present right at Pentecost, wouldn't surprise me if Priscilla and Aquilla were among those. Later Cornelius was a Centurion from Italy, it's safe to say he wound up spending some time later back in Italy. Rome didn't need an Apostolic mission to plant the initial seed of The Gospel there.
From Romans 16 we know Peter wasn't in Rome when Paul wrote to them. Same with Paul's later Epistles written when he was in Rome and occasionally references people there with him, no Peter. Peter has still never left the Near East the last time we see him in Acts.
Romans 1:11 says that while there were Christians there The Church wasn't really established in Rome yet, and it was Paul's mission to go there and establish it. In Romans 15 Paul said he wouldn't be building on another man's foundation.
In Galatians 2:11 Paul mentioned having an encounter with Peter in Antioch. The Christians of Antioch had local traditions of Peter being their "first bishop" also. In fact there were people in Antioch who claimed to be descended from Peter, in fact to this day certain families still claim it. Peter like all of the 12 did have a wife and possibly children.
And then there is First Peter where he clearly says he was in Babylon. I'm amused by those Protestants and Evangelicals who want to use the "Babylon is code for Rome" argument to back up their view of Revelation 17. But the whole origin of that argument was made by the Catholic Church to twist 1 Peter 5:13 into supporting their tradition. Rarely is it acknowledged that there is equally strong regional tradition among Mesopotamian Christians that he meant exactly what he said.
Some people will claim Peter called himself The Apostle to The Gentiles in Acts 15 and use that as evidence he clearly wouldn't have not gone to the capital of the world. But in the KJV, I don't see that in Acts. In 15:7 he refers back to the events of 10-11. But in general the 12's mission was to the Lost Sheep of the House of Israel. Matthias who replaced Judas went to Ethiopia where there were Jews.
"The gospel of the circumcision was unto Peter; (For He that wrought effectually in Peter to the apostleship of the circumcision, the same was mighty in me toward the Gentiles:)" (Gal. 2:7-8). Another Galatians passage calls Cephas, John and James the Apostles of the Circumcision.
Recent investigations of Hellenistic Mesopotamian records have even challenged the view that Babylon shrank in the shadow of Seleucica during the Greeco-Roman period. It was a city with many Jews and Gentiles. Antioch too we know had a strong Jewish population. And he wrote 1 Peter to areas in Turkey, and clearly refereed to the exiles of the dispersion (translated strangers in the KJV) those who were still scattered abroad from the Assyrian and Babylonian exiles.
In addition to the City of Babylon itself there were other Jewish populations in Mesopotamia, the city of Seleucica also had a Jewish Population. As did Nisibis which is a key modern Kurdish capital. As well as Edessa the capital of Osroene. All three of those were among the ones were Jewish uprisings happened during the Kitos War decades later in the reign of Trajan. There was also a Jewish kingdom in Mesopotamia at this time ruled by a proselyte, Adiabene, I don't know whether Peter's letter would have been written during the reign of Izates II or Monobaz II, but it was likely one of those. Some have even speculated that it was specifically Christianity they converted to but that Josephus and the Talmud obscured that fact.
Rome had a Jewish population, but it was not nearly as significant.
Papias statement about the origin of Mark's Gospel does not mention Rome btw, that is just something constantly read into it when people have referenced it. But even how Eusebius quotes it is unclear about where they were when Mark wrote it.
There is a rarely talked alternative fate for Peter's Body.
What I feel like noting is being buried on the Mount of Olives doesn't mean he died near there, Jewish Tradition has often said that is where the Resurrection will begin so being buried on the Mount of Olives is something many Jews have desired. And it's importance in the New Testament means early Jewish Christians could have shared it.
But I find it unlikely that from Italy anyone would have risked trying to transport his body there. There was always a risk traveling the Mediterranean Sea. But from Antioch or Babylon I could find it being fairly plausible. This also hurts the traditions about Lazurus, Martha and Mary of Bethany traveling to southern France, those were always late traditions.
Even a lot of the early sources that do support linking Peter to the Roman church fail to support the entirety of the traditional narrative. Tetullian as I said before says Clement was appointed by Peter, unaware of Linus or Cletus it seems. But he is also our oldest Christian source on Nero persecuting Christians, and doesn't mention Peter or Paul. Eusebius was the first to say that both Peter and Paul were martyred by Nero.
In Tetullian's Apology quoted by Eusebius he doesn't mention Peter or Paul talking about Nero He is cited as backing up the tradition with what he says in his Poscription Against Heretics 34.
"Since, moreover, you are close upon Italy, you have Rome, from which there comes even into our own hands the very authority (of apostles themselves). How happy is its church, on which apostles poured forth all their doctrine along with their blood; where Peter endures a passion like his Lord's; where Paul wins his crown in a death like John's[the Baptist]; where the Apostle John was first plunged, unhurt, into boiling oil, and thence remitted to his island-exile."The problem is we know John's being plunged into oil according to every other source on it happened in Asia not Italy. It looks like copiers may have corrupted something that was originally merely about Rome being responsible for martyrdoms. It's really starting to seem to me like even Paul dying there is questionable. First Clement says nothing of where Paul died, but says he took the Gospel to the extremity of the West.
Eusebius cites a Caius who worked for Bishop Zephyinus of Rome as referring to Apostles being buried on Vatican Hill. The Vatican Hill was a cemetery of Rome's pagan priests, the idea that Peter or Paul would have been buried there is absurd. Even Catholic sources admit it was a pagan cemetery.
"On the night of his death on the cross Peter’s followers BURIED his body. As in the case of Jesus on the hill of Calvary it was wrapped in linen and secretly taken to a PAGAN BURIAL GROUND on the Via Cornelia, behind the stone structure of the arena. This PAGAN CEMETERY lay on a knoll called VATICANUS: the Latin word ‘vatis’ means a ‘prophet’ or ‘SOOTHSAYER’. In days gone by there had been an Etruscan oracle on this spot" (Keller’s comment – the official comment of the Roman Catholic Church p. 368).
In addition to Caius being likely an official propagandist for the Roman Bishop. Eusebius says he said this disputing a Proclus who was advocating the "Phyrgian Hersey" which is what he called the Montanists. So there were early Christians disputing this tradition. I'm not sure how I feel about the Montanists, but dispute did exist Pre-Constantine about Peter being buried in Rome. Phyrgia was in the region 1 Peter was written to, Asia, so they might have known more then most about where it came from.
It's also entirety on Eusebius word that Dionysus of Corinth (around 171) said what Eusebius says he said. Dionysus is the earliest witness that Peter and Paul were in Rome together, something none of even the highly fictionalized and illogical Apocryphal acts of the Apostles claimed.
Peter being in Corinth however briefly is more Bibliclally supportable then being in Rome, Given how he comes up in the Corinthian Epistles. But even that is unclear.
Another early source on Peter in Rome (but later then Dionysus or Caius) was Lactantius. His account of it is awkwardly expressed.
Hippolytus of Rome was a Bishop of Rome, so he had a clear bias for wanting to promote such a false idea.
Also Justin Martyr was the first to mention Simon Magus going to Rome and he doesn't mention Peter being there at the time.