1 The elder unto the wellbeloved Gaius, whom I love in the truth.
[AD 550] Oecumenius on 3 John 1:1
To the beloved Elder Gaius, whom I love in truth.
It has been said in the preceding letter about such a greeting: and now to repeat explaining the same things over the flow would be excessive, "whom I love in truth." He loves in truth who loves with affectionate love according to the Lord: as has also been frequently stated above.

[AD 614] Andreas of Caesarea on 3 John 1:1
John writes this letter to encourage some fellow believers. He writes to Gaius and testifies to his great hospitality, which he praises. He says that someone who does such good is from God. He goes on to tell him to expel Diotrephes, who has not learned to do the same thing. He also praises Demetrius for doing the same as Gaius and mentions his faith as a testimony to his virtue. His main purpose for writing is the same as it was in his second letter.

[AD 735] Bede on 3 John 1:1
The elder to the beloved Gaius, etc. Who and what kind of person this Gaius was, is revealed in the course of the Epistle. Because clearly he accumulated good deeds in addition to the faith in Christ which he had received, and although he was not sufficient for preaching the word himself, he rejoiced to sustain those who did preach with his resources. We believe this Gaius to be the one whom Paul mentions in the Epistle to the Romans, saying: “Gaius, my host and the host of the whole church, greets you” (Rom. XVI). For he was accustomed to be called a host both as one who receives and is received, he was the host of the entire church because he kindly received all who came to him, namely both the preachers and the hearers of the word, as the following parts of this Epistle clearly declare. Hence, John also loves him in the truth, that is, he appears to love him only with the view of eternal goods, not for the sake of temporal benefits. But it seems that Gaius was in Corinth, from the fact that Paul, having stayed in that city, wrote the Epistle to the Romans, whom he greets in his name. And also in the Epistle to the Corinthians, he mentions Gaius as a citizen of Corinth, saying: “I thank my God that I baptized none of you except Crispus and Gaius, lest anyone should say that you were baptized in my name” (I Cor. I).

[AD 1107] Theophylact of Ohrid on 3 John 1:1
He loves in truth who loves according to the Lord.