I don't know who F. A. Sullivan is, and don't know why you think I should consider him authoritative.
It is true that the office of Apostle is superior to that of Bishop, so that St. Peter would hold the office of Bishop of Antioch while keeping all of his authority as an Apostle.
As for his position in Antioch, the 1917 Catholic Encyclopedia notes:
The later tradition, which existed as early as the end of the second century (Origen, "Hom. vi in Lucam"; Eusebius, "Hist. Eccl.", III, xxxvi), that Peter founded the Church of Antioch, indicates the fact that he laboured a long period there, and also perhaps that he dwelt there towards the end of his life and then appointed Evodrius, the first of the line of Antiochian bishops, head of the community. This latter view would best explain the tradition referring the foundation of the Church of Antioch to St. Peter.
It is true that the rank of Apostle is superior to that of Bishop, so that St. Peter would hold the office of Bishop of Antioch while keeping all of his authority as an Apostle.
He's cited in the Catholic Encyclopedia and wrote From Apostles to Bishops
It is true that the office of Apostle is superior to that of Bishop, so that St. Peter would hold the office of Bishop of Antioch while keeping all of his authority as an Apostle.
Holding two offices at the same time was frowned upon in the Scriptures. An apostle was a travelling missionary and founded churches and moved on. Peter travelled around the area as an Apostle while James was probably a bishop or presbyter along with others in Jerusalem. If anyone was the first bishop of Antioch, it would have been Stephen or Barnabas. Does Eusebius mention them?