Since Peter was also Bishop of Antioch, did the successor of Peter in Antioch also possess the charism of infallibility?
No, Peter’s office is singular. The primacy has been understood to have passed on via Rome, where he died, even though he established several Sees. For instance: From Cardinal Ratzinger (now Pope Emeritus Benedict XVI) from April 2005 on Peter’s successors. Excerpt:
Moreover, Eusebius of Caesarea organized the first version of his ecclesiastical history in accord with the same principle. It was to be a written record of the continuity of apostolic succession, which was concentrated in the three Petrine sees Rome, Antioch and Alexandria-among which Rome, as the site of Peter’s martyrdom, was in turn preeminent and truly normative.
No the bishop of Antioch after Peter is not infallible…He is when a member of the College in council in union with the other bishops who are in union with the Pope.
this can be demonstrated by all of Christian History don’t let the Orthodox fool you there is plenty of evidence out there to substantiate this clam. When you start hearing things like forgeries and such they have already lost the argument.
Only when Peter was the Bishop. The charisma of infallibility went with Peter to wherever he went and was passed on when and where he died.