I have read on a blog that Origen argued that Matthew wrote first, Mark wrote second and Luke wrote third. I cannot find any resources on this.
I suspect there is a very good reason. As best as I can find, no surviving work of Origen gives an order and the surviving works that may imply an order are ambiguous e.g. when he refers to Mark as the second Gospel it is not clear whether he means (a) second in order of writing or (b) second in order read in church liturgy.
However, despite finding the above information from a reliable source, I found this translation from a less reliable source:
[quote]
CONCERNING the four Gospels which alone are uncontroverted in the Church of God under heaven, I have learned by tradition that the Gospel according to Matthew, who was at one time a publican and afterwards an Apostle of Jesus Christ, was written first; and that he composed it in the Hebrew tongue and published it for the converts from Judaism. The second written was that according to Mark, who wrote it according to the instruction of Peter, who, in his General Epistle, acknowledged him as a son, saying, “The church that is in Babylon, elect together with you, saluteth you; and so doth Mark my son.”2 And third, was that according to Luke, the Gospel commended by3 Paul, which he composed for the converts from the Gentiles. Last of all, that according to John.
2 1 Pet. 5:13.
3 Or, who is commended by Paul.
Origen, “Origen’s Commentary on the Gospel of Matthew,” in The Gospel of Peter, the Diatessaron of Tatian, the Apocalypse of Peter, the Visio Pauli, the Apocalypses of the Virgil and Sedrach, the Testament of Abraham, the Acts of Xanthippe and Polyxena, the Narrative of Zosimus, the Apology of Aristides, the Epistles of Clement (Complete Text), Origen’s Commentary on John, Books I-X, and Commentary on Matthew, Books I, II, and X-XIV, ed. Allan Menzies, trans. John Patrick, vol. 9, The Ante-Nicene Fathers (New York: Christian Literature Company, 1897), 412.
If you were to conduct a search in Logos in reference to the authorship of Matthew, you would probably find a number of commentaries that direct you to the Church History of Eusebius, perhaps the earliest extant account of the Gospel order according to Origen.
