That he described himself to be a Bishop, in Charge of Affairs External to the Church.

Hence it was not without reason that once, on the occasion of his entertaining a company of bishops, he let fall the expression, “that he himself too was a bishop,” addressing them in my hearing in the following words: “You are bishops whose jurisdiction is within the Church: I also am a bishop, ordained by God to overlook whatever is external to the Church.” And truly his measures corresponded with his words: for he watched over his subjects with an episcopal care, and exhorted them as far as in him lay to follow a godly life.

EusVC 3.222.1