Person keeps coming back into group conversation

This person keeps hacking into my iMessage group conversations and it's really starting to get annoying. Every time I remove him from our conversation, he joins back in and is unkickable. I believe he has a jail broken device, but I do not know what hack he is using. I've searched up this and I can't seem to find anything.

What is he doing and how can I stop him?

He isn't actually hacking into your iMessage at all. Group messages can be a little strange in the way they work. When you remove someone from a group thread there is no way for them to know unless you specifically notify them. It does not show them that they were removed nor does it delete the thread. As such, the other party in your case is likely carrying on business as usual by messaging the group thread that you thought to removed him from. Here's the catch: you did remove him but when he messages the old group it creates a new group thread that looks identical to the one you removed him from. Then, when you remove him again, it goes back to the other thread and he can not see updates.

As such, to resolve your problem, use two, unique group thread names. If you tap "Details" in the upper right, and scroll up a little you will see a field to name the group. Find the one he is part of and the one he is not part of and then name them differently. Then inform the others on the thread he is not on to use [thread name] for messaging not [thread name with unwanted user].

Finally, if you want no correspondence from the unwanted guest, you can block him, but that will sever all communications. Moreover, you will not receive any of his messages yet the other members of your group chat will if they haven’t blocked him.