Adam Clarke on Acts 23:2

The high priest, Ananias - There was a high priest of this name, who was sent a prisoner to Rome by Quadratus, governor of Syria, to give an account of the part he took in the quarrel between the Jews and the Samaritans; see Joseph. Antiq. lib. xx. cap. 6, s. 8; but whether he ever returned again to Jerusalem, says Dr. Lightfoot, is uncertain; still more uncertain whether he was ever restored to the office of high priest; and most uncertain of all whether he filled the chair when Paul pleaded his cause, which was some years after Felix was settled in the government. But Krebs has proved that this very Ananias, on being examined at Rome, was found innocent, returned to Jerusalem, and was restored to the high priesthood; see Joseph. Antiq. lib. xx. cap. 9, s. 2; but of his death I find nothing certain. See Krebs on this place, (Observat. in Nov. Testament. e Flavio Josepho), who successfully controverts the opinion of Dr. Lightfoot, mentioned at the beginning of this note. There was one Ananias, who is said to have perished in a tumult raised by his own son about five years after this time; see Jos. Antiq. lib. x. cap. 9. War, lib. ii. cap. 17.

To smite him on the mouth - Because he professed to have a good conscience, while believing on Jesus Christ, and propagating his doctrine.