According to the Synaxarion of Constantinople, two saints associated with the military were commemorated on January 3rd in the Eastern Roman Empire - St. Theagenes of Parium and St. Gordius of Caesarea in Cappadocia. St. Theagenes of Parium is described as a Bishop who was being held in prison for refusing to enter into military service, since he considered himself to be a servant and soldier of Christ. St. Gordius of Caesarea was a centurion, who abandoned his office because as a Christian he could no longer endure to hear the name of Christ blasphemed, and became a hermit outside the city. Both are said to have lived under Emperor Licinius in the early fourth century and were martyred. Both are also described as having rejected earthly military service to serve as a soldier of God instead. Why were both Saints commemorated on January 3rd?
One possible answer may have its source in the so-called Feriale Duranum, a fragmentary papyrus copy of the official Roman military religious calendar, which was discovered among the records of the cohors XX Palmyrenorum at Dura Europus, and dates to the period c.223/7 A.D. It includes the following description of the ritual to be observed on 3 January:
January 3. Because vows are paid and undertaken both for the welfare of our Lord Marcus Aurelius Severus Alexander Augustus and for the eternity of the empire of the Roman nation, [to Jupiter Optimus Maximus an ox, to Juno Regina a cow, to Minerva a cow, to Jupiter Victor] an ox, [to Juno Sospes? a cow, --- to Mars Pater a bull, to Mars Victor] a bull, to Victoria a cow.
This is generally identified now as the occasion of the annual renewal by the soldiers of their oath of allegiance to the emperor, the sacramentum which each conscript took at the end of his probationary period before he was posted to his final unit. It was of this oath that Tertullian famously wrote:
Incompatible are the human oath of allegiance and the divine sacrament, the standard of Christ and the standard of the devil, the legions of the light and the legions of the darkness. One soul cannot serve two lords: God and Caesar.
The Christian emperors of the fourth century retained the oath of allegiance, but in a Christianized form which made it clear that allegiance to the emperor was second to one's allegiance to God, which clarification must have disarmed the objections of many to the oath itself. If this oath continued to be renewed on 3 January, and there is no reason to think that this was not the case, then the decision by the author of the Passion of Saint Theagenes to date the death of Saint Theagenes to 3 January would seem particularly appropriate in the case of a martyr who was alleged to have rejected earthly military service for the service of God. So the choice of this date represents a continuation of the theme of the Passion itself, the need to choose between God and Caesar, essentially making it a pacifist text. No servant of the state could read of Saints Theagenes and Gordius and fail to marvel that they had been executed for their rejection of military service on the very day that soldiers were accustomed to renew their oath of allegiance. It was a direct challenge, in fact, to all Christians in the military, or at least the more pious individuals who had attended a church-service earlier that day, not to proceed with the renewal of their oath of allegiance, but to take the opportunity offered them and reject earthly service for that of the divine King. Or perhaps it merely spoke only of not being in military service under a non-Christian ruler in a non-Christian environment.
Today, while Saint Gordius is still commemorated in the Orthodox Church on January 3, the feast of Saint Theagenes was moved to the day before, on January 2, for unknown reasons. The Synaxarion of Constantinople has him listed under January 3, but the edition of Saint Nikodemos the Hagiorite has him commemorated on January 2.