Are the teachers and prophets who laid hands on Saul & Barnabas in Acts13:1-3 ordained Bishops? Some Catholics justify St. Paul’s apostolic succession by citing Acts 13:1-3:


  Now in the church at Antioch there were prophets and teachers: Barnabas, Simeon called Niger, Lucius of Cyrene, Manaen (who had been brought up with Herod the tetrarch) and Saul. While they were worshiping the Lord and fasting, the Holy Spirit said, “Set apart for me Barnabas and Saul for the work to which I have called them.” So after they had fasted and prayed, they placed their hands on them and sent them off.


St. Paul’s testimony on Galatians 1:1-2 seems to contradict Acts 13:1-3:


  Paul, an apostle—sent not from men nor by a man, but by Jesus Christ and God the Father, who raised him from the dead— and all the brothers and sisters with me


To clear out the contradiction, does the  Church have a record who ordained St. Paul or did St. Peter ordain St. Paul?

If no one from Apostles ordained St. Paul, then St. Paul testimony on Galatians 1:1 prevails.

Is there a clear explanation on this two passages?
”And when they had fasted and prayed, and laid their hands on them, they sent them away. - Acts 13:3”


The passage does not tell exactly what is the laying of hands. Is it a blessing prayer for their journey or a sacramental ceremony? Let’s take a look on what is says in this commentary below.


  Fasting and prayer, imposing their hands upon them. By which is clearly expressed, the manner in which the ministers of God were, and are still ordained bishops, priests, deacons in the Church. (Witham) 
  Interpreters are much divided in opinion, whether this imposition of hands be a mere deputation to a certain employment, or the sacramental ceremony, by which orders are conferred. Sts. Chrysostom, Leo are of the latter opinion; nor does it any where appear that St. Paul was bishop before this. Arator, sub-deacon of the Church of Rome, who dedicated in the year 544 his version of the Acts of the Apostles into heroic verse to Pope Virgilius, attributes this imposition of hands to St. Peter: 
  
  -Quem mox sacra it euntem Imposita Petrus ille manu, cui sermo magistri Omnia posse dedit.
  
  See his printed poems in 4to. Venice, an. 1502. Arator was sent in quality of ambassador from Athalaric to the emperor Justinian. 
  Following the practice of the apostles, the Church of God ordains a solemn and general fast on the four public times for ordination, the ember days, as a necessary preparation for so great a work, and this St. Leo calls also an apostolical tradition. See St. Leog, serm. ix. de jejun. and ep. lxxxi. chap. 1. and serm. iii. and iv. de jejun. 7. mensis.
  Nor was this fasting a fasting from sin, as some ridiculously affirm, for such fasting was a universal obligation: nor was it left to each one's discretion, as certain heretics maintained. See St. Augustine, hæres. liii.
  
  
  George Leo
  
  
  “2. And as they were ministering to the Lord and fasting, the Holy Ghost said to them: Separate me Saul and Barnabas, for the work whereunto I have taken them.
  And when they had fasted and prayed, and laid their hands on them, they sent them away. - Acts 13:3”


Here is another commentary that explains further:


  What means, Ministering? Preaching. Separate for Me, it says, Barnabas and Saul. What means, Separate for Me? For the work, for the Apostleship. See again by what persons he is ordained (γυμνοτέρα . Cat. σεμνοτέρα, more awful.) By Lucius the Cyrenean and Manaën, or rather, by the Spirit. The less the persons, the more palpable the grace. He is ordained henceforth to Apostleship, so as to preach with authority. How then does he himself say, Not from men, nor by man? Galatians 1:1 Because it was not man that called or brought him over: this is why he says, Not from men. Neither by man, that is, that he was not sent by this (man), but by the Spirit. Wherefore also (the writer) thus proceeds: So they, being sent forth by the Holy Ghost, departed unto Seleucia; and from thence they sailed to Cyprus.
  
  
  John Chrysostom