How Would an Early Christian “Know” Which Books Peter Wrote?

So if there were lots of books in circulation that claimed to be written by the apostle Peter, why did some of them (1 and 2 Peter) come to be accepted both as his and as canonical scripture, and others come to be deemed forgeries and excluded from the canon?

The first point to stress is that Christians in the second, third, and fourth centuries had no real way of knowing which, if any, of these books Peter wrote.  They were living many decades or even centuries after the books had first been...