Legal Question in Landlord & Tenant Law in New Jersey

Technically the mailbox belongs to the federal government. You receive the delivery of your mail as a free service. That is conditioned on the presence of a mailbox conforming to federal regulation. That being said, you can make whatever arrangement you need to make as far as mail distribution is concerned. In answer to your question specifically, you can require as part of the lease, the mail distribution that you are talking about. That is leaving your tenants mail at the bottom of the stairs. I don't know if this is an oral arrangement between you and the tenant or if it's a written agreement.

In New Jersey, since you share the building with the tenant and it is less than three units, you can get rid of your tenant for any reason. If it is more than three units, you are subject to the Anti-Eviction Act (AEA) and there are 20 grounds to evict. Habitual late payment of the rent is a basis to evict under the AEA. Either way you have a basis to evict.

Without knowing more about your situation, there may be other options available. Most attorneys in this field will offer a free consult for one half hour to discuss your situation and see what options you may have.