If you accidentally paid twice, you should be able to contact the State of New Jersey (a contact link is below) and request that they refund the excess amount to you.  You may be asked to write a letter or fill out a form.  

Often a state will refund an excess payment automatically when they process your return, but sometimes it gets treated as an estimated payment for the next year. 

https://www.state.nj.us/treasury/revenue/revgencode.shtml