How did the early church fathers refute Adoptionism?

Adoptionism had been declared a heresy by the Synod of Antioch in A.D. 268, which meant that neither Lucian, Arius, nor Eusebius could openly embrace it. After that Synod, anyone who dared claim that Jesus Christ was not in any sense God but only a human prophet adopted by God into a special, unique, relationship would likely lose their church position, if not be exiled by the emperor.

Adoptionism was attributed to Paul of Samosata. In Adoptionism (as in Nestorianism) the uncreated Son of God never enters into human existence. Paul of Samosata taught that Jesus’ divinity could be explained by his special relationship with God the Father beginning with his baptism in the River Jordan. He viewed the already-existing doctrine of the eternal deity of Christ as threatening the monotheism of Christianity. He believed that Jesus Christ was a man adopted by God as his special human son, which did not require Christ to actually become God. This reduced Christ to being a great prophet. Paul of Samosata was deposed by his own people after the condemnation of the Synod of Antioch in 268.

Those who were later taught by Lucian of Antioch (died 312), such as Arius, might not have had (or expressed) fully blown Adoptionist beliefs, but they found ways of less openly denying the fully divine status of the uncreated Son of God by saying he had been created by God at some point in time therefore, “there was a time when he was not.” Similar to Adoptionism, the teaching was that the Son remain forever subordinate to the Father not only in terms of his role but also in terms of his very Being.

You wish to know how the early church fathers refuted Adoptionism, so this rules out the debates of the Council of Nicea in 325 or thereafter. The pre-268 declaration of that heresy appealed to various proofs as to the full deity and uncreated status of the Son of God, the New Testament having such teachings by the Apostles. John, for instance, had written that the Word, who became flesh as the man, Jesus, was with God in the beginning, was God, and that the Word made everything that was made (John 1:1-14). He further wrote in the Revelation given to him by the resurrected Christ that this Lamb of God was [effectively] slain from the foundation of the world due to the agreement in the Godhead that this would happen (Rev. 13:8). And the risen Christ receives the worship of all heaven’s creatures, who fall before one throne crying, “Worthy is the Lamb that was slain to receive power, and riches, and wisdom, and strength, and honour and glory, and blessing. And every creature which is in heaven, and on the earth, and under the earth, and such as are in the sea, and all that are in them, heard I saying, Blessing, and honour, and glory, and power unto him that sitteth upon the throne, and unto the Lamb, for ever and ever.” (Rev. 5:12-13).

Unfortunately, I have drawn a blank with my books as to the deliberations of that Synod of Antioch. Although Boniface Ramsey in his 1985 book, Beginning to Read the Fathers, has a chart of Patristic Chronology, and he lists the Council of Antioch condemning Paul of Samosata, 268, there is a blank in the adjacent column of ‘Fathers and Patristic Writings’.

Although you said you are looking for “council documents (not necessarily the 798 AD council, if adoptionism happened to be addressed at an earlier council)”, I have pointed out that Adoptionism was first condemned at the 268 Council, so that the answer needs to focus on that time period. And Ramsey has no mention of any Fathers and Patristic Writings then. You alluded to Pope Victor 1st (A.D. 190-198, claimed as being the first black pope). He was known for how he excommunicated churches for celebrating Easter based on the Jewish date of Passover and not on a Sunday. Eventually he reversed his decision. I couldn’t find anything on-line about his views on Adoptionism. However, this link shows that it needs to be the writings of the Apostolic Fathers that should be consulted, given that they wrote up to that time period when Adoptionism was first condemned at the Council of Antioch. https://www.gotquestions.org/Apostolic-Fathers.html

As pointed out in the comments following the question, the connection with all of this to modern groups calls for alertness to many mutations over the centuries. Adoptionism and Arianism are alive and well in disparate groups, such as Unitarianism, liberalism, and the Jehovah’s Witnesses. They all have their variations on those old ideas that various Councils condemned, so modern versions are often an amalgam of different points from different ancient groups. For example, Jehovah’s Witnesses do emphasise Jesus’ special relationship with God the Father beginning with the baptism in the River Jordan, but then mix in Arius’s points about Jesus being a created angel, prior to that. The Unitarians are closer to Paul of Samosata in denying Christ’s pre-human existence. That is why it can be helpful to know Church history from the end of the 1st century onward