Admittedly, it's a convoluted question. Having said that, the basic idea is: from when to when were you working in New York, and from when to when were you making the interest payments? If all of your income was earned in New York throughout the year, and all of the income was earned in New York, then you input the total interest paid as the New York Portion, because you made all of the student loan interest payments off of the NY income.
Another case: Let's say you only paid interest from January to June, and you started working in NY in July. In this case the amount of interest against the NY nonresident income is zero.
Anything in between requires a prorate. For instance, if you were working in NY and CT at the same time, you would have to prorate the deduction by percentage between the two. (Example: you earned 5,000 in CT and 20000 in NY. Your interest payment on NY nonresident income is 2,000. Or, let's say that you made student loan interest payments between January and June, and earned income in NY between April through December. Since not all of the interest payments were made against NY income, you would have to subtract out the interest paid before April from the portion paid while earning NY nonresident income.
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