Confidently for constantly, A.V. (for the same use of διΐσχυρίζομαι, see Luke 22:59); and they said for then said they, A.V. It is his angel; meaning probably his guardian angel (Matthew 18:10). But the expression is obscure, and we do not know exactly the nature of the belief on which it was grounded.
They must have thought that perhaps Peter had been put to death in prison that very night, and that his angel, speaking with his voice, was sent to announce it to the Church. The narrative is a striking instance how "slow of heart to believe" are even the most devout.
They were praying very earnestly for Peter's life; their prayer was granted; and yet the announcement of it only draws out the answer, "Thou art mad!" and then, as an alternative, the explanation, "It is his angel!"