Since you do use the Church Fathers in your studies, please refer to the citations made in this post for Patristic references to Peter being in Rome and having founded the Church there.
The Simon Peter referred to by the ECF was obviously Simon "Magus" Pater....and the ECF were..... obviously mistaken here. It has been pointed out by me that "These Twelve" were instructed not to go (evangelize) the Gentiles [Matthew 10:5]. I will choose scripture over ECF!
I never said that the ECF writings were divinely inspired. I said I use them for historical reference as I do Josephus, Herodotus and others.