As far as I know, from my readings of Church Fathers, Saul's encounter were
First: seeing The Christ on the road to Damascus in a vision
“And I answered, Who art thou, Lord? And he said unto me, I am Jesus of Nazareth, whom thou persecutest.” Acts 22:8, KJV.
Second: a vision in Jerusalem where he was given his marching orders,
“And he (The Lord) said unto me, Depart: for I will send thee far hence unto the Gentiles.” Acts 22:21, KJV.
Third: during his visit to the third heaven that same year.
“I knew a man in Christ above fourteen years ago, (whether in the body, I cannot tell; or whether out of the body, I cannot tell: God knoweth;) such an one caught up to the third heaven. And I knew such a man, (whether in the body, or out of the body, I cannot tell: God knoweth;) How that he was caught up into paradise, and heard unspeakable words, which it is not lawful for a man to utter.” 2 Corinthians 12:2-4, KJV.
And here it is agreed by many Church Fathers that Paul is talking about himself.
None of the Fathers is quoted as saying that Saul/Paul met with Jesus in the flesh. In the NT, Paul only quotes Jesus once, in reference to the Eucharist. So this shows his ignorance of Jesus.
Whether Paul met Jesus or not is a moot point. Christianity went ahead without reference to Judaism - only they borrowed the Prophets, and the Psalms, from the Septuagint, needed to give scriptural support to the New Testament theology. A sort of re-reading of the Hebrew scripture that fit the New ideas. This Old Testament, which the Hebrews considered to be heresy, was incorporated into the Christian Bible during the 4th. cent.
Paul called his theology "my Gospel." Ro 2:16; 16:25; 2Ti 2:8. And we know if was different from the Gospel of the Apostles because the Pauline writings talk of the clashes with those from Jerusalem "who teach another Gospel." What the Church in Jerusalem taught (under James the Just, the brother of Jesus,) has been swept under the carpet, so to speak. What The Church is founded upon are teachings from the Pauline community.
For the nascent Christian/Pauline Church to prosper outside the Holy Land, it was important to turn over control of the Church to the Greeks, who had developed a theology which had The Risen Christ at its center, not Jesus the Messiah, who was a descendant of David, and not divine, but anointed to be King of Judea - hence "Jesus annointed." In Hebrew it was " Yeshuah Messiach," in Greek "Ihsous Christos", all meaning anointed one (this was the theology of the Jerusalem Church and later the Ebionites.)
The Greek (later Roman) Church's revolutionary idea was called "The New Testament," - it came from the teaching of the Pauline Community, whose writings reached the Church in Rome in 140.
Without Paul, there would have been a Hebrew-Christian Church probably similar to those who vowed poverty, later called the Ebionites by their detractors, which religion died out by the 4th. cent. (but some scholars say later than this.)
Eventually the Hebrew disciples were driven from the Church by legalisms, and Judaism with them, including their God Yahweh (this is a simplification of what happened.) Without a God to call their own, Jesus was declared to be God - a declaration that didn't suit all the Bishops. And for another two hundred years, the various Christian churches ( there were some fifty denominations) fought over whether Jesus was human or divine, a man or God.
In the 4th. cent. Bishop Eusebius was empowered by the Pagan Emperor Constantine to bring all the Bishops of the Empire together to settle on one understanding of God. About 300 attended. All Bishops were required to declare that Jesus was God incarnate, or suffer excommunication. Only six objected, and were excommunicated (later re-instated as power was handed over to a new Bishop.)
By very skilful argument at this council of Nicea (as it became known,) almost all the Bishops were convinced that: Jesus, The Father, and the Holy Ghost were consubstatial - of the same essence but different personas. The Trinity in Unity was born in AD 325. It was tacitly understood that the Hebrew understanding of God had been incomplete.
Even today in my classes, some people say that the Hebrew God of wrath and justice, is not the same as the loving and merciful God of Christianity.
Almost everyone in Protestant America thinks that Paul had the correct understanding of what Christianity should be - despite the fact that, unlike the twelve, he never met Jesus, and never studied under him.
I expect a lot of flack with this posting. But: "Blessed are the peacemakers," Jesus said, so be patient.