The headword, in the genitive case (extracted from the quotation given), is Latin curiosus: LSJ Supplement s.v. kouriw=sos, Lampe s.v. kouriw=sos "official informer to the Emperor", Trapp s.v. kouriosso/s. Moore (1921) fn. 39: "The Curius was the responsible guardian to whom was entrusted the care of minors and women (cf. our word curate): so Curiosus is any functionary employed by a superior official, in this case the comes, for a public duty."
[1] John Chrysostom, Letter I to Pope Innocent PG 52.532 (spelled kouriw/sou in the that Migne edition), on the first exile of Chrysostom; also cited in Palladius, Dialogue on the Life of Chrysostom p. 11 Coleman-Norton. As translated by Moore (1921; web address 1), "Late one evening, when I was being escorted through the streets by the whole of the populace, I was arrested by the city governor's agent in the middle of the city, dragged away by force, and put on board a ship, which set sail by night; when I was summoning a synod for a just trial."