score:6
I would suggest the answer is found in the book of the Acts of the Apostles. There, Paul shared the gospel in various ways, such as popular culture (Acts 17:23, the unknown god) and local poetry (17:28).
Then later he gave his personal testimony to the Jews of how Christ saved him and gave him a new purpose in life (22:1ff). Later he was taken and put in a cell, and there the Lord appeared and indicated that He was pleased with Paul's testimony of Him in Jerusalem. What's curious to me is that Jesus did not mention all the other cities in which he had preached. It was in Jerusalem before the Jews that he gave his testimony.
After that we find him giving his testimony again in 26:12 before Agrippa. Perhaps he had put two and two together and saw that reciting his personal encounter was more significant to the Lord, so he used that approach with Agrippa. Unfortunately, the book of Acts closes soon with no more mention about this approach. He was mainly a teacher and to the end taught from the Scriptures that Jesus was the Christ, and how people must repent for the kingdom of God.
I know you wanted examples from the church fathers on, but these few examples (and an example or two from the epistles) should be taken into account as probable origins of bearing one's personal testimony. After all, we do draw instruction from the Word of God. Paul gave his testimony without giving up teaching; he found a place for both.
Upvote:2
The roots may be understood to go back as far as the ministry of Jesus on earth. After casting out demons from a certain man, Jesus basically tells him to share his testimony of what Jesus had done in his life:
And all the people of the country of the Gerasenes and the surrounding district asked Him to leave them, for they were gripped with great fear; and He got into a boat and returned. But the man from whom the demons had gone out was begging Him that he might [j]accompany Him; but He sent him away, saying, “Return to your house and describe what great things God has done for you.” So he went away, proclaiming throughout the whole city what great things Jesus had done for him. Luke 8:37-39 NASB
This was also true for the man who had been blind from birth. The religious leaders are contending with Him about the identity of Jesus, when he falls back to his personal testimony:
He then answered, “Whether He is a sinner, I do not know; one thing I do know, that though I was blind, now I see.” John 9:25 NASB
The apostle Paul also shares his personal testimony of how he came to faith in Jesus Christ on two different occasions that are recorded in the book of Acts (Acts 22, Acts 26), and perhaps many more times that are not recorded.
So, it may have been reintroduced as a prominent part of evangelism by certain people in the past 2,000 years, but its root seems to go back to even before the resurrection.