Well, the apology should be to the ones you unfairly banned. Go and unban anyone on any stream that you banned unfairly. This is your chance to start fresh and do the right thing. Thank you.
I recommend posting an apology meme in the begging stream in order to make amends and hopefully restore trust and good relations. make it genuine and sincere.
I allowed you to be a moderator with the agreement that you would abide by stream rules. This will be your only warning. If I hear that you are unfairly banning people you will not be moderator and will be banned as well. Is this clear?