From page 33 of the instructions for Form NJ-COJ:
"When claiming a credit for taxes paid to New York, the amount on line 1 must reflect the “New York State Amount” actually taxed by New York from the New York IT-203."
https://www.nj.gov/treasury/taxation/pdf/current/1040i.pdf#page=33
With TurboTax be sure to complete your non-resident NY tax return before you do your home state NJ tax return. The problem should then calculate the "other jurisdiction tax credit" for you.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
