part year NJ resident move to NYC. Do I put new york as work on credit or leave it blank for jurisdiction NYC

[Vanessa A]

If you were a part year NJ resident and then you moved to NYC, you would file a Part Year Return for both NY and NJ.  

Where did you work while living in each state?  If you worked in NY while living in NJ, you would take a credit on your NJ taxes for taxes paid to NY while living in NJ or vice versa if you lived in NY and worked in NJ.  You would only take a credit for the time you lived in the state that you did not work in.