20 All the brethren greet you. Greet ye one another with an holy kiss.
[AD 220] Tertullian on 1 Corinthians 16:20
But when is peace more to be concluded with brethren than when, at the time of some religious observance, our prayer ascends with more acceptability; that they may themselves participate in our observance, and thereby be mollified for transacting with their brother touching. their own peace? What prayer is complete if divorced from the "holy kiss? " Whom does peace impede when rendering service to his Lord? What kind of sacrifice is that from which men depart without peace? Whatever our prayer be, it will not be better than the observance of the precept by which we are bidden to conceal our fasts; for now, by abstinence from the kiss, we are known to be fasting.

[AD 384] Ambrosiaster on 1 Corinthians 16:20
The holy kiss is the sign of peace, doing away with discord.

[AD 407] John Chrysostom on 1 Corinthians 16:20
4. "All the brethren salute you. Salute one another with an holy kiss." This addition of the "holy kiss" he makes only here. What may the reason be? They had been widely at variance with one another on account of their saying, "I am of Paul, and I of Apollos, and I of Cephas, and I of Christ;" on account of "one being hungry, and another drunken;" on account of their having contentions and jealousies and suits. And from the gifts there was much envying and great pride. Having then knit them together by his exhortation, he naturally bids them use the holy kiss also as a means of union: for this unites, and produces one body. This is holy, when free from deceit and hypocrisy.

[AD 407] John Chrysostom on 1 Corinthians 16:20
Having bound them together by his exhortation, Paul goes on to bid them to set the seal on their union by means of the holy kiss, which unites and produces one body. The kiss is holy when it is free of deceit and hypocrisy.