I now have a copy of Stephen C. Carlson’s Papias of Hierapolis Exposition of Dominical Oracles: The Fragments, Testimonia, and Reception of a Second Century Fragment (Oxford: Oxford University Press, 2021). It is a fantastic work that helpfully assesses the reliability of a large number of references to Papias during the Patristic and Medieval eras. I know that he plans to follow up his translations of the fragments with a commentary. Also check out his “Fragments of Papias” in The Cambridge Companion to the Apostolic Fathers (ed. Michael F. Bird and Scott Harrower; Cambridge: Cambridge University Press, 2021) and his interview about Papias with Michael Bird. Previously, he wrote several guest posts about Papias at Bart Ehrman’s blog (see here, here, here, here, here, here, here). Here is a brief bibliography on the fragments of Papias:

• Carlson, Stephen C. Papias of Hierapolis: Exposition of Dominical Oracles: The Fragments, Testimonia, and Reception of a Second Century Fragment. Oxford: Oxford University Press, 2021.
• Ehrman, Bart D. Apostolic Fathers. 2 vols. Loeb Classical Library. Cambridge, MA: Harvard University Press, 2003.
• Holmes, Michael W. Editor and Translator. The Apostolic Fathers in English. Third Edition. Grand Rapids: Baker Academic, 2006.
• Körtner, Ulrich H. J. Papias von Hierapolis: Ein Beitrag zur Geschichte des frühen Christentums. FRLANT 1303. Göttingen: Vandenhoek & Ruprecht, 1983.
• Kürzinger, Josef. Papias von Hierapolis und die Evangelien des Neuen Testaments. Regensberg: Pustet, 1983.
• Lightfoot, J. B. and Harmer, J. R. The Apostolic Fathers: Revised Texts with Short Introductions and English Translations. London: Macmillan, 1891.
• MacDonald, Dennis. Two Shipwrecked Gospels: The Logoi of Jesus and Papias’s Exposition of Logia about the Lord. Atlanta: Society of Biblical Literature, 2012.
• Norelli, Enrico. Papia di Hierapolis: Esposizione degli Oraculi del signore: I Frammenti. Milan: Paoline, 2005.
• Schoedel, William R. Polycarp, Martyrdom of Polycarp, Fragments of Papias. The Apostolic Fathers: A New Translation and Commentary 5. New York: Nelson, 1967.
• Shanks, Monte A. Papias and the New Testament. Eugene, OR: Pickwick, 2013.

Here are some important articles on Papias:

• Annand, Rupert. “Papias and the Four Gospels.” Scottish Journal of Theology 9 (1956): 46–62.
• Bartlet, Vernon. “Papias’s ‘Exposition’: Its Date and Contents.” Pages 15-44 in Amicitiae Corolla: A Volume of Essays Presented to James Rendel Harris, D. Litt. on the Occasion of his Eightieth Birthday. Edited by H. G. Wood. London: University of London Press, 1933.
• Bauckham, Richard. “Papias and Polycrates on the Origin of the Fourth Gospel.” Journal of Theological Studies 44.1 (1993): 24-69.
• Baum, Armin. . “Ein aramäische Urmatthäus im kleinasiatischen Gottesdienst. Das Papiaszeugnis zur Entstehung des Matthäusevangeliums.” Zeitschrift für die Neutestamentliche Wissenschaft 92 (2001): 257–72.
• Black, Matthew. “The Use of Rhetorical Terminology in Papias on Mark and Matthew.” Journal for the Study of the New Testament 37 (1989): 31–41.
• Carlson, Stephen. “Eschatological Viticulture in 1 Enoch, 2 Baruch, and the Presbyters of Papias.” Vigiliae Christianae (2017)
• Colson, F. H. “Τάξει in Papias (The Gospels and the Rhetorical Schools).” Journal of Theological Studies 14 (1912): 62–69.
• Deeks, David G. “Papias Revisited.” Expository Times 88 (1977): 296–301, 324–29.
• Furlong, Dean. “Theodore of Mopsuestia: New Evidence for the Proposed Papian Fragment in Hist. eccl. 3.24.5–13.” Journal for the Study of the New Testament 39.2 (2016): 209-229.
• Grant, Robert M. “Papias and the Gospels.” Harvard Theological Review 25 (1943): 208-22.
• Grant, Robert M. “A Note on Papias.” Anglican Theological Review 29 (1974): 171-72.
• Gundry, Robert H. “The Apostolically Johannine Pre-Papian Tradition
  Concerning the Gospels of Mark and Matthew.” Pages 49-73 in The Old is Better: New Testament Essays in Support of Traditional Interpretations. WUNT 178. Tübingen: Mohr Siebeck, 2005.
• Heard, Richard. “APOMNĒMONEUMATA in Papias, Justin and Irenaeus.” New Testament Studies 1 (1954): 122–29.
• Hill, Charles E. Papias of Hierapolis.” The Expository Times 117 (2006): 309–15.
• Hill, Charles E. “What Papias Said about John (and Luke): a New ‘Papian’ Fragment.” The Journal of Theological Studies 49 (1998): 582–629.
• Kennedy, George. “Classical and Christian Source Criticism.” Pages 125-155 in The Relationship among the Gospels: an Interdisciplinary Dialogue. Edited by William O. Walker. San Antonio: Trinity University Press, 1978.
• Manor, T. Scott. “Papias, Origen, and Eusebius: The Criticisms and Defense of the Gospel of John.” Vigiliae Christianae 67 (2013) 1–21.
• Mommsen, Theodor. “Papianisches.” Zeitschrift für die Neutestamentliche Wissenschaft 3 (1902) 156–59.
• Mullins, Terence Y. “Papias on Mark’s Gospel.” Vigiliae Christianae 14
  (1960): 216–24.
• Mullins, Terence Y. “Papias and Clement and Mark’s Two Gospels.” Vigiliae Christianae 30 (1976): 189–92.
• Munck, Johannes. “Presbyters and Disciples of the Lord in Papias.” Harvard Theological Review 52 (1959): 223–43.
• Nielsen, Charles M. “Papias: Polemicist Against Whom?” Theological Studies 35 (1974): 529–35.
• Perumalil, A. C. “Are Not Papias and Irenaeus Competent to Report on the Gospels?” Expository Times 91 (1980): 332–37.
• Riggs, Horace A. “Papias on Mark.” Novum Testamentum I (1956): 161–83.
• Siegert, F. “Unbeachtete Papiaszitate bei armenischen Schriftstellern.” New Testament Studies 27 (1981) 605–14.
• Stewart-Sykes, Alistair. “Taxei in Papias: Again.” Journal of Early Christian Studies 3.4 (1995): 487-492.
• Wright, Arthur. “Taxei in Papias.” Journal of Theological Studies 14 (1913): 298–300.
• Yarbrough, R. W. “The Date of Papias: A Reassessment.” Journal of the Evangelical Theological Society 26 (1983): 181–91.

I have a review of Dean Furlong’s The John also Called Mark: Reception and Transformation in Christian Tradition (WUNT 2.518; Tübingen: Mohr Siebeck, 2020) for the Catholic Biblical Quarterly. Furlong has some helpful summaries of his chapters, as well as his other articles, at his academia.edu page and you can read an interview about his work The Logos Academic Blog. If you are not a subscriber to the journal, you can read an excerpt from my review here that summarizes the thesis of the book that the John who was surnamed Mark in the book of Acts was not the evangelist Mark nor the first bishop of Alexandria, but should be identified as the author of the fourth canonical Gospel (i.e. the evangelist John). He has another book entitled The Identity of John the Evangelist: Revision and Reinterpretation in Early Christian Sources. His view is that the Apostle John was martyred early on in fulfilment of Jesus’s predictions that he would drink his cup and receive his baptism of suffering, while John Mark lived to old age in Ephesus where he authored the Gospel of John and was known to his fans as the Elder John.

Ultimately, I am not persuaded that the earliest Patristic writers did not identify the author of the second canonical Gospel (i.e. the evangelist Mark) as the “(John) Mark” appearing in the pages of the New Testament (cf. Acts 12:12, 25; 13:1; Phlm 1:24; Col 4:10; 2 Tim 4:11; 1 Pet 5:13), though I have argued that Mark was not associated closely with Peter until the late first century, and I also think that the Patristic authors who attributed the fourth canonical Gospel to “John the disciple of the Lord” probably meant the Apostle John rather than the Elder John. Nevertheless, I concluded my review by stating that Furlong’s “hypotheses merit further testing, but his command over a wide range of Christian literature is impressive and his monograph is a must-read reception history of the character of John/Mark.” Indeed, I learned so much from the extensive data that Furlong has compiled from Christian literature throughout the Patristic and Medieval periods and I would interpret it as evidence of how frequently John Mark was confused with the evangelist John because they had the same name.

Here is a preview of what I will be working on this semester:

• A chapter in an edited volume building on the case that Jesus’s act of walking on the sea displays his imperial, Davidic, messianic identity. I think that this book, which is based on a conference I attended in Sydney, should be published sometime this year and I will give more details when it is available.
• An article arguing that while Justin Martyr identifies the Synoptic Gospels as “the memoirs of the apostles” and was likely familiar with Papias’s tradition (e.g., identifying Mark’s Gospel as Peter’s memoirs), there is no evidence that he had any knowledge of the attribution of the third canonical Gospel to the Evangelist Luke. This will be an open-access article in the Journal of Greco-Roman Christianity and Judaism that will be available by the end of 2021.
• An article looking at how scholarship on the Carpocratians has developed since Morton Smith’s reconstruction of them, which will also critique Smith’s handling of the heresiological data and interpretation of the Letter to Theodore. This article will be published for Ephemerides Theologicae Lovanienses by the end of 2021.
• I am currently working on a paper about Jewish Christians during the Patristic period and a rough draft of a book about the traditions on the Evangelist Matthew that I hope will result in publications.