It is 100%. Your NY state refund is entirely based on New York source income, because you filed a nonresident return with New York. If the situation were reversed (asking about a NJ refund), the amount of the refund is affected by the amount of credit that NJ gives for the tax you pay to NY on that income. But in this case, the question is how much of the NY state refund is from New York Sources. The answer is all of it.
It is 100%. Your NY state refund is entirely based on New York source income, because you filed a nonresident return with New York. If the situation were reversed (asking about a NJ refund), the amount of the refund is affected by the amount of credit that NJ gives for the tax you pay to NY on that income. But in this case, the question is how much of the NY state refund is from New York Sources. The answer is all of it.
does that mean you put 0 on the box..or the total federal amount?
You will put the entire amount of the income that was earned in New York state. You enter the amount, not the percentage.
You can see the amount that your employer reported for NY State earnings in Box 16 on your W-2 form. That is the amount that you use to attribute wages earned in the state.
You won't need to worry about paying income tax in multiple states, even if you have to file more than one return. When you live in one state and work in another, the state where you work usually gets to tax you and will withhold the appropriate amount from your paycheck each week.