I just went through the above site: It confirmed my memory of my courses at Evangel College:
None of the First Century writers mentioned Peter as bishop of Rome. The mentions of him were either quotes from the gospel, or allusions to Peter as an apostle.
. . . BTW, you keep changing the criteria - moving the target. You are the one who started with the 4th century, now you're down to the first century A.D. . . Our Saviour's death and resurrection didn't occur until half way through that century. That tells me you lack confidence in your sources . . . and that lack of confidence is well founded.