If you want an introduction to Ignatius, the early second century bishop of Antioch who sent letters to various Christ congregations while on route to Rome where he would be martyred, check out the work of William R. Schoedel, Allen Brent, and Paul Foster. Paul Foster has also written the chapter “The Epistles of Ignatius of Antioch and the Writings that Later Formed the New Testament” in The Reception of the New Testament in the Apostolic Fathers (ed. Andrew F. Gregory and Christopher M. Tuckett; Oxford: Oxford University Press, 2005), 159-186. He covers the reception of Matthew’s Gospel in Ignatius’s letters on pages 173-181. He begins with an overview of the debate over whether Ignatius was directly dependent on Matthew’s Gospel (e.g., Massaux, Köhler) or not (e.g., Koester, Sibinga, Hagner) (173). Adopting Koester’s method of searching for traces of Matthew’s redactional work in the letters of Ignatius, thus confirming Ignatius’s dependence on Matthew’s Gospel itself rather than Matthew’s sources, Foster arrives at the following results:
The explanation that Jesus was baptized by John “in order that all righteousness might be fulfilled by him” in Smyrneans 1.1 reminds one of Jesus’s response to John that his baptism was necessary “to fulfil all righteousness” (3:15). Matthew’s phrase may be redactional as he likely added the dialogue to deal with Mark’s “embarrassing” account of Jesus’s baptism by John, Luke does not reproduce the dialogue so it is unlikely that it was part of Q if Q contained a baptism account, and righteousness is a favourite term that Matthew uses in singly attested traditions (e.g., Matt 5:20) and adds to his sources (Matt 5:6/Luke 6:21; Matt 6:33/Luke 12:31) (174-75). Foster rejects Koester’s alternative proposal that Ignatius was indirectly influenced by Matthew’s redaction in that the phrase may have been lifted from Matthew’s text and repeated in another oral context where the bishop heard it (175-76). He also rejects Sibinga’s argument that a pre-Matthean form of the phrase (i.e. “all things to be fulfilled”) is attested in the Gospel of the Ebionites (cf. Epiphanius, Panarion 30.13.8), which agrees with Ignatius in using the passive form of the verb, for Epiphanius may not have cited the verse accurately, the wider passage that he cites seems to harmonize the Synoptic baptism narratives (cf. 30.13.7-8), and Ignatius is closer to Matthew in using the term “righteousness” (176).
In Trallians 11.1 and Philadelphians 3.1, Ignatius warns his readers to stay away from people who were not planted by the Father. The saying is phrased differently in each passage and the agreements with Matthew 15:13 are restricted to the words for “plant” (phyteia) and “father” (patēr) and the negative clause (177). Foster allows that Matthew could have either inserted a free-floating saying into a Markan context or redactionally created it himself (cf. compare Matt 15:1-20 with Mark 7:1-23) and points out that Ignatius does not cite the saying in Matthew’s literary context (177), so he sides with Koester against Massaux and Köhler that these passages do not prove Ignatius’s dependence on Matthew’s Gospel rather than another written or oral source (e.g., perhaps he heard it in a homily) (177-78).
Ignatius advises the bishop Polycarp to be as shrewd as a snake and innocent as a dove (Polycarp 2.2), which is paralleled in Matthew 10:16 but also logion 39 in the Gospel of Thomas (178). The first part of the logion has parallels to Luke 11:52, which may also have been in the Q source (cf. Luke 11:52/ Matt 23:13). Thus, depending on one’s judgment regarding whether the Gospel of Thomas provides independent attestation for these sayings that show up in a different form in the Gospels of Matthew and Luke or was conflating the Synoptic verses will impact the decision over whether Ignatius could have known a pre-Matthean form of the saying or depended on Matthew 10:16 (178-79).
Finally, Ignatius’s expression ho chōrōn chōreito (“the one who receives, let him receive” ) in Smyrneans 6.1 shares three words in common with Matthew 19:12d, except Matthew has the participle ho dunamenos (“the one who is able”) followed by the infinitive chōrein (“to receive”). This gnomic saying follows a difficult proposition in both cases, but Matthew was encouraging acceptance of Jesus’s teaching on divorce and celibacy while Ignatius wanted his readers to accept that cosmic judgment would be based on one’s response to the blood of Christ (179). Foster again agrees with Koester that the short saying could have circulated orally in a homiletic context (180).
Foster concludes that there is only one “certain example” of Ignatius’s dependence on Matthew’s Gospel (i.e. Smyrn. 1.1/Matt 3:15) (180). Other examples are less certain, but they may help in advancing a cumulative case for Ignatius’s knowledge of the Gospel of Matthew (181), whereas Ignatius’s knowledge of the other three Gospels cannot be established with any degree of certainty (181-84). In the The New Testament in the Apostolic Fathers, W. R. Inge had listed some further parallels that he gives either a “c” rating (Eph. 5.2/Matt 18:19-20; Eph. 6.1/Matt 10:40; Pol. 1.2-3/Matt 8:17) or a “d” rating (Eph. 17.1/Matt 26:7; Magn. 5.2/Matt 22:19; Magn. 9.3/Matt 18:52; Rom. 9.3/Matt 10:40-41), but he finds most of the suggested parallels apart from perhaps the first one to be “totally unconvincing” (180). Christine Trevett noted that 36 possible allusions to Matthew’s text have been proposed by scholars, though only 18 of these receive sustained attention, but many of them are rather “extremely faint allusions” (174). Interestingly, the dependence of Ignatius and the Gospel of the Ebionites on Matthew 3:15 came up for debate after I presented my paper at SBL. It could be objected that Ignatius does not place the saying in the context of a conversation with John and the Gospel of the Ebionites lacks the key term “righteousness,” but I think that the difficulty that interpreters may have had with explaining how Jesus’s baptism exemplified “righteousness” lead Ignatius to recontextualize it (i.e., all the saving events of Jesus’s life that truly happened including his baptism fulfil all righteousness) and the author of the Gospel of the Ebionites to drop “righteousness” (i.e. Jesus’s baptism fulfils the things prophesied).