Peter was in Antioch, as bishop, for seven years before he moved to Rome.
Acts 11:
1 Now the apostles and the believers who were in Judea heard that the Gentiles had also accepted the word of God. 2 So when Peter went up to Jerusalem, the circumcised believers criticized him,…
20 But among them were some men of Cyprus and Cyrene who, on coming to Antioch, spoke to the Hellenists also, proclaiming the Lord Jesus.
Acts 11
:22 News of this came to the ears of the church in Jerusalem, and they sent Barnabas to Antioch…
25 Then Barnabas went to Tarsus to look for Saul, 26 and when he had found him, he brought him to Antioch. So it was that for an entire year they met with the church and taught a great many people, and it was in Antioch that the disciples were first called "Christians…
29 The disciples determined that according to their ability, each would send relief to the believers living in Judea; 30 this they did, sending it to the elders by Barnabas and Saul.
Byzcath, Peter was in Judea, and it was the Apostle Paul and other disciples who were at the church in Antioch. They sent “relief” up to the elders (Peter being there also) in Judea.
The Catholic Church teaches that the first Bishops of the Church were the Apostles, of which Paul was one.
Acts 15:22
Then the apostles and the elders, with the consent of the whole church, decided to choose men from among their members and to send them to Antioch with Paul and Barnabas. They sent Judas called Barsabbas, and Silas, leaders among the brothers,
Acts 15:35
But Paul and Barnabas remained in Antioch, and there, with many others, they taught and proclaimed the word of the Lord.
Galatians 2:11
But when Cephas (Peter) came to Antioch, I opposed him to his face, because he stood self-condemned;
Now, some online sites state different men as being the first bishop of Antioch, - for example:
christian-history.org/theophilus.html
Theophilus was a bishop of Antioch, Paul’s home church in Scripture. He’s the second bishop of Antioch that we have writings from. Ignatius was the first.
A Patriarchial church claims:
orthodoxwiki.org/Church_of_Antioch
The Church of Antioch is the continuation of the Christian community founded in Antioch by the Apostles Peter (who served as its first bishop) and Paul, who are its patron saints. In terms of hierarchical order of precedence, it currently ranks third among the world’s Orthodox churches, behind Constantinople and Alexandria.
The seat of the patriarchate was formerly Antioch (Antakya), in what is now Turkey. Now it is in Damascus, Syria, located on the “street called Straight.” The current patriarch is His Beatitude Patriarch Ignatius IV (Hazim) of Antioch and all the East.
the Catholic Encyclopedia source (which come from Early church Father writings):
newadvent.org/cathen/05653a.htm
The first Bishop of Antioch after St. Peter. Eusebius mentions him thus in his “History”: “
And Evodius having been established the first [bishop] of the Antiochians, Ignatius flourished at this time” (III, 22). The time referred to is that of Clement of Rome and Trajan, of whom Eusebius has just spoken. Harnack has shown (after discarding an earlier theory of his own) Eusebius possessed a list of the bishops of Antioch which did not give their dates, and that he was obliged to synchronize them roughly with the popes. It seems certain that he took the three episcopal lists of Rome, Alexandria, and Antioch from the “Chronography” which Julius Africanus published in 221. The “Chronicle of Eusebius” is lost; but in Jerome’s translation of it we find in three successive years the three entries
•that Peter, having founded the Church of Antioch, is sent to Rome, where he perseveres as bishop for 25 years;
•that Mark, the interpreter of Peter, preaches Christ in Egypt and Alexandria; and
•that Evodius is ordained first Bishop of Antioch.
I trust what the Bible says, and those sources from the Early church fathers.
Peter, with Paul, founded the Church of Antioch, but it was Peter, as history records, who established Evodius as first Bishop of Antioch.