Exposition of the Old and New Testament, by John Gill, [1746-63], at sacred-texts.com
Though this epistle was called in question and gainsaid by some as authentic, as Eusebius says (a), yet there is no room to doubt of the authority of it; it was very early received into the canon of the Scripture, and is cited as such, and also as the Apostle John's, by Irenaeus (b), who was a disciple of Polycarp, and an hearer of Papias, who were both disciples of the Apostle John; nor need there be any question as to his being the author of it. Eusebius indeed does say (c), it was a doubt whether it was the Apostle John's or another of the same name; and some have since asserted, that it was written not by John the Evangelist, but by John the Presbyter of Ephesus, after the apostle; and this is thought to have some confirmation from the author of it being called an elder, or presbyter, which is judged not so agreeable to the Apostle John; though it should be observed, that Peter an apostle styles himself an elder, as John here does, Pe1 5:1, moreover, the above ancient writer, Irenaeus, expressly ascribes this epistle to John, the disciple of the Lord; and whoever compares some passages in this epistle with the former, particularly Jo2 1:5, with Jo1 2:7, will easily conclude, from the likeness of style and matter, that it is a genuine epistle of the Apostle John: the design of which is to exhort and encourage the lady he writes to, to continue in the truth and faith of the Gospel, and in love to God and his people, and to avoid false teachers and their doctrines.
(a) Eccl. Hist. l. 3. c. 24. (b) Adv. Haeres. l. 1. c. 13. & l. 3. c. 18. (c) Adv. Haeres. l. 3. c. 25.