People are not hit in prison are they? Unless they are being beaten up by inmates.
You take something they like away from them for a brief period of time, or make them do something they dislike.
Example: if a child writes on the wall, give them a sponge and make them wash it, even if it takes hours. Hitting them doesn't send the message across as it doesn't last long and after they cry a bit they get on with their day, without facing any real consequences of their actions.
Example, if you are taking the kids to the park, the child that's naughty stays home with dad and does extra homework. Firmly tell the child why they are being punished and that they can only avoid this punishment next time if they don't engage in that sort of behaviour. That is much more likely to have a lasting impact than hitting them in anger.
Ok this is a middle age white woman. Extra home work? Thats child abuse and no somali would do that to their child. What are we Chinese? I would call social service on you for that