Peter, as an apostle, had supreme jurisdiction over all Christians...as did the other apostles.

As "apostle to the Jews", he had a special, prototype patriarchy, over Jewish Christians, as did Paul over gentiles.

The famous "rebuke" issue shows Peter's position: EVERYONE, including Paul's man Barnabas, followed Peter's lead. And Peter didn't even SAY anything!!!

The papal supremecy issue doesn't concern rank and file Christians. Rather, it's only a matter vis a vis Peter and the other apostles.

Same with bishops in general. All Christians are under their bishop and patriarchs. The papacy really only concerns the relation of the pope and other bishops, for, as I said, Christians are already under their local bishops.

The whole Christian Church has historically recognized several Patriarchs of the Church. The Bishop of Rome is one such Patriarch: the Patriarch of the Western Church. All Christians in the western rite are under this Patriarch...regardless of the papacy issue.

For the papacy issue really only involves the Patriarch of the Western Church vs the various Patriarchs in the East.

As for Peter in Rome, you and I have already been over this, rather desperate, cannard you keep throwing out.