Start here:

1. Complete Part XI of Federal information worksheet including state residency status and dates.

2. use Quick Zoom to Part Year Resident State Allocation worksheet and allocate the wages, etc. 

3. on NY information worksheet PART II select Part year resident IT203... you'll have to do some allocating here too but if you follow the error flags the program does a pretty highlighting fields that need to be addressed... 

4. When you clear the errors then try NJ.  (Note; be sure to check the wages in NJ box 15  are correct.  Depending on how the W2 worksheets are completed, the wages that transfer can double.... if that's the case double click on line 15 to get to statement for wages, salaries.... THEN enter income attributed to NY PY Res .... OR you can double click on income from all sources (line 1) to get to total wages worksheet where you can exclude duplicate state wages (often times NY state taxable wages differ from NJ taxable wages b/c NJ taxes cafe125s, 414h, and lots of stuff that IRS and NY do not.