A periodeutes, or periodeutai was a kind of specially-ordained visiting priest in various Eastern churches.
The fifty-seventh canon of the Synod of Laodicea (380) prescribed that the chorepiscopi should be replaced by periodeutai, i.e., priests who have no fixed residence and act as organs of the city bishops.
In the Maronite Church, a periodeutes or bardūt is "a kind of vicar forane who acts for the bishop in the inspection of the rural clergy."
References
Periodeutes Wikipedia(Text) CC BY-SA