[~100 AD] Fragments of Papias (from his 5 books called Expositions of Oracles of the Lord)
Papias' works did not survive to the present day, we only can see fragments of his works as quoted by others.
The modern comprehensive volume of the fragments of Papias is " Papias of Hierapolis Exposition of Dominical Oracles ", by Stephen C. Carlson.
However given that it costs enough to empty your wallet, we instead turn to other sources. Dr. TC Schmidt , an Assistant Professor of New Testament and Early Christianity at Fairfield University, did some extensive research on Papias earlier in his career and published it online .
Also worth reviewing:
http://www.hypotyposeis.org/synoptic-problem/2004/10/external-evidence-papias.html
https://web.archive.org/web/20060202001319/http://www.mindspring.com/~scarlson/synopt/ext/papias.htm
https://peterkirby.com/putting-papias-in-order.html
https://www.ewtn.com/catholicism/library/fragments-of-papias-12534
Table of Contents
[AD 180] Irenaeus of Lyons
The predicted blessing, therefore, belongs unquestionably to the times of the kingdom, when the righteous shall bear rule upon their rising from the dead; when also the creation, having been renovated and set free, shall fructify with an abundance of all kinds of food, from the dew of heaven, and from the fertility of the earth: as the elders who saw John, the disciple of the Lord, related that they had heard from him how the Lord used to teach in regard to these times, and say: The days will come, in which vines shall grow, each having ten thousand branches, and in each branch ten thousand twigs, and in each true twig ten thousand shoots, and in each one of the shoots ten thousand clusters, and on every one of the clusters ten thousand grapes, and every grape when pressed will give five and twenty metretes of wine. And when any one of the saints shall lay hold of a cluster, another shall cry out, "I am a better cluster, take me; bless the Lord through me." In like manner [the Lord declared] that a grain of wheat would produce ten thousand ears, and that every ear should have ten thousand grains, and every grain would yield ten pounds (quinque bilibres) of clear, pure, fine flour; and that all other fruit-bearing trees, and seeds and grass, would produce in similar proportions (secundum congruentiam iis consequentem); and that all animals feeding [only] on the productions of the earth, should [in those days] become peaceful and harmonious among each other, and be in perfect subjection to man.
And these things are borne witness to in writing by Papias, the hearer of John, and a companion of Polycarp, in his fourth book; for there were five books compiled (συντεταγμένα) by him. And he says in addition, "Now these things are credible to believers." And he says that, "when the traitor Judas did not give credit to them, and put the question, 'How then can things about to bring forth so abundantly be wrought by the Lord.' the Lord declared, 'They who shall come to these [times] shall see.'"
[AD 303] Eusebius of Caesarea
[ Note from Dr. TC Schmidt : My translation. Eusebius wrote his Chronicon in the year 303AD. I am fairly certain that the Greek for this passage comes from an unattributed quotation from George Syncellus’ Chronology 424. When it is matched with Jerome’s translation of Eusebius, it seems certain that this is what Eusebius said.]
Chronicon 220th Olympiad/100AD
Irenaeus and others record that John the Theologian and Apostle survived until the times of Trajan; after which Papias of Hierapolis and Polycarp, bishop of Smyrna, both of whom heard him, became well known.
In the third year of the reign of the emperor mentioned above, Clement committed the episcopal government of the church of Rome to Evarestus, and departed this life after he had superintended the teaching of the divine word nine years in all.
But when Symeon also had died in the manner described, a certain Jew by the name of Justus succeeded to the episcopal throne in Jerusalem. He was one of the many thousands of the circumcision who at that time believed in Christ.
At that time Polycarp, a disciple of the apostles, was a man of eminence in Asia, having been entrusted with the episcopate of the church of Smyrna by those who had seen and heard the Lord.
And at the same time Papias, bishop of the parish of Hierapolis, became well known, as did also Ignatius, who was chosen bishop of Antioch, second in succession to Peter, and whose fame is still celebrated by a great many.
1. There are extant five books of Papias, which bear the title Expositions of Oracles of the Lord. Irenæus makes mention of these as the only works written by him, in the following words: "These things are attested by Papias, an ancient man who was a hearer of John and a companion of Polycarp, in his fourth book. For five books have been written by him." These are the words of Irenæus.
2. But Papias himself in the preface to his discourses by no means declares that he was himself a hearer and eye-witness of the holy apostles, but he shows by the words which he uses that he received the doctrines of the faith from those who were their friends.
3. He says: But I shall not hesitate also to put down for you along with my interpretations whatsoever things I have at any time learned carefully from the elders and carefully remembered, guaranteeing their truth. For I did not, like the multitude, take pleasure in those that speak much, but in those that teach the truth; not in those that relate strange commandments, but in those that deliver the commandments given by the Lord to faith, and springing from the truth itself.
4. If, then, any one came, who had been a follower of the elders, I questioned him in regard to the words of the elders — what Andrew or what Peter said, or what was said by Philip, or by Thomas, or by James, or by John, or by Matthew, or by any other of the disciples of the Lord, and what things Aristion and the presbyter John, the disciples of the Lord, say. For I did not think that what was to be gotten from the books would profit me as much as what came from the living and abiding voice.