I believe you remove the NY amount from the NJ return, but it's probably good to check that you have followed the process for part-year returns correctly. These articles may help:
https://ttlc.intuit.com/questions/1901227-how-do-i-file-a-part-year-state-return
https://ttlc.intuit.com/questions/2895983-how-do-i-allocate-split-income-for-a-part-year-state-retur...
https://ttlc.intuit.com/questions/2895965-how-does-turbotax-calculate-taxes-on-part-year-returns
