The Letter to the Ephesians
The Letter to the Magnesians
The Letter to the Trallians
The Letter to the Romans
The Letter to the Philadelphians
The Letter to the Smyrnaeans
The Letter to Polycarp, Bishop of Smyrna
They are mentioned both by Eusebius and by Jerome. In the nineteenth century the ones we have were often thought spurious on the (somewhat dubious) basis that their ecclesiology was so robust, but it was discovered that the common versions, usually known as the Long Rescension, were probably interpolated revisions of another, less well known version, the Middle Rescension, and the arguments against the earliness of the Long Rescension, whatever their status, did not really apply to the Middle Rescension.
On reaching Rome, at some point around AD 108, St. Ignatius was martyred. In Antioch his feast was celebrated on his traditional martyrdom day, October 17, and this spread throughout the Church, although slowly the feast drifted in various calendars to other days (February 1 in the West, December 20 among the Eastern Orthodox); the new calendar for the ordinary form reverts to the ancient memorial, which had continually been kept by some churches of the Syrian tradition.
From his epistle to the Ephesians (Chapter 10):
Pray continually for the rest of humankind as well, that they may find God, for there is in them hope for repentance. Therefore allow them to be instructed by you, at least by your deeds. In response to their anger, be gentle; in response to their boasts, be humble; in response to their slander, offer prayers; in response to their errors, be steadfast in the faith; in response to their cruelty, be civilized; do not be eager to imitate them. Let us show by our forbearance that we are their brothers and sisters, and let us be eager to be imitators of the Lord, to see how can be the more wronged, who the more cheated, who the more rejected, in order that no weed of the devil may be found among you, but that with complete purity and self-control you may abide in Christ Jesus physically and spiritually.
[Michael Holmes, ed. & tr., The Apostolic Fathers, Baker Academic (Grand Rapids, MI: 2007) pp. 191-192.]