My question involves landlord-tenant law in the State of: New Jersey

Rented out my apartment, but tenant is not living up to my standards. The tenant paid first and last month's rent upon move in. The tenant already paid for this month, but I want to give this person 30 days notice now. If I give notice, Am I liable to pay back three weeks of the last month's rent as the move-out date will be the first week of next month?