When was it first said in Christianity by a Church Father that heretics must be put to death? Who was the first one of the Church Fathers who came up with this idea and presented it?
Technically, the first ecclesiastical authority to say that heretics should be persecuted was Pope Gregory IX in 1229. The first Church Father to say that heretics should be compelled to recant would be Augustine around 400 AD.
The first heretic actually put to death (385AD) was killed by the Emperor - and the Pope was very annoyed at the development. It wasn't for another 800 years that the church followed suit.
The church typically did not execute heretics. Rather, the state, sometimes at the behest of the church or other times of a monarch desiring no discord amongst his subjects, would carry out such persecution and executions.
The earliest Christian heretics were not put to death by the Church, but rather by the Roman Empire. Note for example, the first "heretic" to be executed - Priscillian - was put to death not by the church, but rather the state. Furthermore, those responsible for getting the state to put him to death were subsequently excommunicated by the Pope for their actions.
Per this article:
Per Wikipedia on heresy:
As a little bit of a side-note... There is a correlation between putting heretics to death and burning them to death. The only thing that was ever supposed to be carried out by the church was excommunication, which technically is the same thing as being put to death in the spirit, which is simply what being put to death by fire actually means.
Let me explain: When a person received the "Word of God" and joined the church, they were received not only by baptism, but they were also received by the "laying on of hands". This procedure is what Jesus had the disciples do for those who desired to have full fellowship in the congregation of the Saints. This is the same thing as receiving the "Gift of the Holy Ghost", receiving "spiritual rebirth" or receiving "spiritual resurrection". This is in fact the resurrection that Jesus brought and established for the salvation of both Jews and Gentiles. First to the Jews and then to the Gentiles.
So, for a person to be "excommunicated", they were officially cast out of the congregation of Saints, which brought with it the revocation of the laying on of hands and their baptism by fire. Thus, they were "denied the Holy Ghost", so to speak, because it is the reception into the "true church" that brings with it the gift of the Holy Ghost. Therefore, they lost their "spiritual life" or "resurrection" and became "spiritually dead" which is the "second death" or being cast out into a lake of fire and brimstone, etc.
By virtue of the church eventually burning people at the stake for heresy, it is clear they had lost their pure original understanding of their mission and purpose as the early apostles were ordained and commissioned. This leads up to the many prophesies that speak of a time in the future when there would first come a period of falling away and that people would have to be willing to "lose their lives" for the sake of the pure Gospel of Jesus Christ. There would come a day when in order for individuals to hold true to the pure Gospel of Jesus Christ that they would have to be willing to be excommunicated from the orthodoxy who would usurp the seats of authority in the Church of Christ.