Is my action considered arrogance and a sin if I hit someone who misbehaved, knowing that I have authority and feel regret afterwards?

We advise the questioner to abandon arrogance and pride, for greatness and majesty belong to Allah alone, and he should remember his origin and weakness. Self-confidence is not arrogance unless it is accompanied by contempt for others. The questioner erred in his feeling of greatness, in punishing someone before their guilt was proven, and in striking them on the face, which is forbidden. He must repent from all of that, and part of complete repentance is to contact the person he struck and ask for their forgiveness.