When it comes to the desire of some Christians to flirt with deeming certain Extra-Biblical texts quasi authentic, The Book of Jasher is the big one since it's the one perceived as being quoted by The Bible itself.
Now I don't know what the Book of Jasher in Joshua 10:13 and II Samuel 1:18 was, but I know it's not any book available today with that name.
The main text people cling to is one that scholars recognize as a medieval rabbinic text. That has 90 or so Chapters and chronicles the history of the world from Creation down to the time of Joshua. It's dates seem to agree with the Masoretic text over the Septuagint or Samaritan Pentateuch (which a Medieval Jewish produced text would) though it makes the mistake of viewing Abraham as born when Terah was 70 rather then 60 years later. The New Testament in Acts 7 clarifies this by making clear Abraham left Haran at 75 when Terah died.
A lot of people like it. They like it verifying the assumption that Nimrod was evil. But it makes lots of claims about Historical Chronology that are frankly absurd.
Here is the death nail, on the subject of the two quotes, the Samuel one could make sense. But with the Joshua one, you need to first understand that in Joshua 10 it's not the narrative voice citing Jasher it's Joshua's own quoted speech.
The Book of Jasher's narrative goes past the point in History where he made that Speech. And the only thing in it that seems like what Joshua could have been quoting is Jasher 88:63-64, which is in fact it's own account of those same events. Not a Prophecy of them written before they happened. In fact it is recording the same speech minus the citing of Jasher.
So it makes no sense, it cannot possibly be what Joshua was quoting.
I would absolutely expect a forgery to include those quotes. It's surprising to me how bad this forger was at deciding how to incorporate the Joshua one.
The so called Jashers are all collections of Jewish Fables. Which Paul told us to pay no heed to in Titus 1:14.
Chapter 9 says Nimrod created 12 idols and named then after the 12 months of the year. This clearly shows a post Babylonian Exile origin as it was after the Exile that the Hebrew months took their current names. some at least came from Babylonian gods, like Tammuz. Those weren't their original names however.
Jasher identifies Nimrod with Amraphel which is stupid. Also Jasher refers to Melchizedek of Genesis 14 not by that name but as Adonizedek, a villain from the Book of Joshua. That I think is very suspicions.
In chapter 12 Jasher included the extra-Biblical legend of Abraham being thrown not a fiery furnace. A legend that is known to have it's origin in an Aramaic mistranslation of "Ur Kassadim" (Ur of the Chaldeans) in Genesis 15. Just read Abraham and the Flame of the Chaldeans. I'm not sure how much I agree with the traditional assumption of which City, but it was a City.
This Jasher's author was clearly familiar with Manetho as he clearly wanted to make Melol seem like Pepi II.
But in chapter 77 this book claims it was the custom of all Kings of Egypt to take the name Pharaoh, that is wrong. The Bible is a large part of why we use that word how we do, it wasn't till the 19th Dynasty that the Egyptians started using it as a name or title for their King. Originally it was just a word for the house the King of Egypt lived in, The Bible using it how it does is basically the same as referring to The President of the United States as The White House.
If the real Book of Jasher whatever it was, was Inspired Scripture God would have preserved it. And if He had preserved it, it would have been included in the Masoretic Hebrew Canon. It is not so it was not.
Jasher 1:19-20 Contradicts Genesis teaching that Man was not allowed to Eat Meat before The Flood.