What are the rules, for terminating a super of an apt building and having him vacate the apt

Unless you and he have a contract that specifically spells this out, you first fire him from the job (do it in writing) and end his tenancy separately, by giving written notice and by going through eviction if necessary, also according to any contract such as a lease, and the laws of your state. Where is this? What if any contract and lease do you have?

Most will have a written contract, don't know I have ever seen one without one. So you follow it.
But agreed, you first have to fire them. At that point you will start the eviction proceedings.

We have no contract, employment at will, and the apt was condition of employment there was no lease and we are in NJ