A Commentary, Critical, Practical, and Explanatory on the Old and New Testaments, by Robert Jamieson, A.R. Fausset and David Brown  at sacred-texts.com
jo3 0:0AUTHENTICITY.--That these two Epistles were written by the same author appears from their similarity of tone, style, and sentiments. That John, the beloved disciple, was the author of the Second and Third Epistles, as of the First Epistle, appears from IRENÃUS [Against Heresies, 1.16.3], who quotes Jo2 1:10-11; and in [3.16.8], he quotes Jo2 1:7, mistaking it, however, as if occurring in First John. CLEMENT OF ALEXANDRIA (A.D. 192) [Miscellanies, 2.66], implies his knowledge of other Epistles of John besides the First Epistle; and in fragments of his Adumbrations [p. 1011], he says, "John's Second Epistle which was written to the virgins (Greek, "parthenous"; perhaps Parthos is what was meant) is the simplest; but it was written to a certain Babylonian named the Elect lady." DIONYSIUS OF ALEXANDRIA (in EUSEBIUS [Ecclesiastical History, 7.25]) observes that John never names himself in his Epistles, "not even in the Second and Third Epistles, although they are short Epistles, but simply calls himself the presbyter, a confutation of those who think John the apostle distinct from John the presbyter. ALEXANDER OF ALEXANDRIA cites Jo2 1:10-11, as John's [SOCRATES, Ecclesiastical History, 1.6]. CYPRIAN [Concerning the Baptism of Heretics], in referring to the bishops at the Council of Carthage, says, "John the apostle, in His Epistle, has said, if any come to you" (Jo2 1:10); so that this Epistle, and therefore its twin sister, Third John, was recognized as apostolic in the North African Church. The MURATORI fragment is ambiguous. The Second and Third Epistles were not in the Peschito or old Syriac version; and COSMAS INDICOPLEUSTES in the sixth century says that in his time the Syriac Church only acknowledged three of the Catholic Epistles, First Peter, First John, and James. But EPHREM THE SYRIAN quotes the Second Epistle of John. EUSEBIUS [Ecclesiastical History,] reckons both Epistles among the Antilegomena or controverted Scriptures, as distinguished from the Homologoumena or universally acknowledged from the first. Still his own opinion was that the two minor Epistles were genuine, remarking, as he does in Demonstration of the Gospel [3.5], that in John's "Epistles" he does not mention his own name, nor call himself an apostle or evangelist, but an "elder" (Jo2 1:1; Jo3 1:1). ORIGEN (in EUSEBIUS [Ecclesiastical History, 6.25]) mentions the Second and Third Epistles, but adds, "not all admit (implying that most authorities do) their genuineness." JEROME [On Illustrious Men, 9] mentions the two latter Epistles as attributed to John the presbyter, whose sepulcher was shown among the Ephesians in his day. But the designation "elder" was used of the apostles by others (for example, PAPIAS, in EUSEBIUS [Ecclesiastical History, 3.39]), and is used by Peter, an apostle, of himself (Pe1 5:1). Why, then, should not John also use this designation of himself, in consonance with the humility which leads him not to name himself or his apostleship even in the First Epistle? The Antilegomena were generally recognized as canonical soon after the Council of Nicea (A.D. 325). Thus CYRIL OF JERUSALEM, A.D. 349, enumerates fourteen Epistles of Paul, and seven Catholic Epistles. So GREGORY NAZIANZEN, in A.D. 389. The Councils of Hippo, 393, and Carthage, 397, adopted a catalogue of New Testament books exactly agreeing with our canon. So our oldest extant Greek manuscripts. The Second and Third Epistles of John, from their brevity (which ORIGEN notices), and the private nature of their contents, were less generally read in the earliest Christian assemblies and were also less quoted by the Fathers; hence arose their non-universal recognition at the first. Their private nature makes them the less likely to be spurious, for there seems no purpose in their forgery. The style and coloring too accord with the style of the First Epistle.
TO WHOM ADDRESSED.--The Third Epistle is directed to Gaius or Caius; whether Gaius of Macedonia (Act 19:20), or Gaius of Corinth (Rom 16:23; Co1 1:14), or Gaius of Derbe (Act 20:4), it is hard to decide. MILL believes Gaius, bishop of Pergamos [Apostolic Constitutions, 7.40], to be the person addressed in Jo3 1:1.
The address of the Second Epistle is more disputed. It opens, "The elder unto the Elect lady" (Jo2 1:1). And it closes, "The children of thy elect sister greet thee" (Jo2 1:13). Now, Pe1 1:1-2, addresses the elect in Asia, &c., and closes (Pe1 5:13), "The Church that is at Babylon, elected together with you, saluteth you." Putting together these facts, with the quotations (above) from CLEMENT OF ALEXANDRIA, and the fact that the word "Church" comes from a Greek word (kyriake) cognate to the Greek for "lady" (kyria; "belonging to the Lord," kyrios); WORDSWORTH'S view is probable. As Peter in Babylon had sent the salutations of the elect Church in the then Parthian (see above on CLEMENT OF ALEXANDRIA) Babylon to her elect sister in Asia, so John, the metropolitan president of the elect Church in Asia, writes to the elect lady, that is, Church, in Babylon. NEANDER, ALFORD, and others, think the Greek "kyria" not to mean "lady," but to be her proper name; and that she had a "sister, a Christian matron," then with John.
DATE AND PLACE OF WRITING.--EUSEBIUS [Ecclesiastical History, 3.25] relates that John, after the death of Domitian, returned from his exile in Patmos to Ephesus, and went on missionary tours into the heathen regions around, and also made visitations of the churches around, and ordained bishops and clergy. Such journeys are mentioned, Jo2 1:12; Jo3 1:10, Jo3 1:14. If EUSEBIUS be right, both Epistles must have been written after the Apocalypse, in his old age, which harmonizes with the tone of the Epistles, and in or near Ephesus. It was on one of his visitation tours that he designed to rebuke Diotrephes (Jo3 1:9-10).