Nicene and Post-Nicene Fathers, Ser. II, Vol. XIV:
The Canons of the Councils of Ancyra, Gangra, Neocæsarea, Antioch and Laodicea, which Canons were Accepted and Received by the Ecumenical Synods.: Canon X

Canon X.

The Holy Synod decrees that persons in villages and districts, or those who are called chorepiscopi, even though they may have received ordination to the Episcopate, shall regard their own limits and manage the churches subject to them, and be content with the care and administration of these; but they may ordain readers, sub-deacons and exorcists, and shall be content with promoting these, but shall not presume to ordain either a presbyter or a deacon, without the consent of bishop of the city to which he and his district are subject.  And if he shall dare to transgress [these] decrees, he shall be deposed from the rank which he enjoys.  And a chorepiscopus is to be appointed by the bishop of the city to which he is subject.

Notes.

Ancient Epitome of Canon X.

A chorepiscopus makes Exorcists, Lectors, Subdeacons and Singers, but not a presbyter or a deacon without the bishop of the city.  Who dares to transgress this law let him be deposed.  The bishop of the city makes the chorepiscopus.

For the Minor Orders in the Early Church see the Excursus on the subject appended to Canon XXIV. of Laodicea.

“Ordination to the episcopate.”  In translating thus I have followed both Dionysius and Isidore, the former of whom translates “although they had received the imposition of the hand of the bishop and had been consecrated bishops;” and the latter “although they had received from bishops the imposition of the hand, and had been consecrated bishops.”

Van Espen.

There can be no doubt that the Chorepiscopi, the authority of whom is limited by this canon, are supposed to be endowed with the episcopal character.  Among the learned there is a controversy as to whether Chorepiscopi were true bishops by virtue of the ordination to that office, and endowed with the episcopal character or were only bishops when accidentally so.  But whatever may be the merits of this controversy, there can be no doubt from the context of this canon that the Fathers of Antioch took it for granted that the chorepiscopi were true bishops by virtue of their ordination, but it is also evident that they were subject to the bishop of the greater city.  It must also be noted that these chorepiscopi were not instituted by the canons of the Councils of Ancyra, Neocæsarea, or even of Nice, for these speak of them and make p. 114 their decrees as concerning something already existing.

And from the very limitations of this canon it is by no means obscure that the fathers of Antioch supposed these chorepiscopi to be real bishops, for otherwise even with the license of the bishop of the city they could not ordain presbyters or deacons.