What you are seeing is how New York calculates tax for a part-year resident. All of your income is not taxed in New York, but all of the income you earned is used to determine how much New York tax you pay. New York will pretend that all of your income is taxed in New York, figure out what the hypothetical tax is on that amount, and then prorate the tax to the percentage of income you received while living (and working) in New York. All of your income is not taxed in New York, but all of your income is reported on the New York return to determine the New York tax.
Is there a deduction for that? The only deduction on a state return is if you are working in New York while living in another state other than New York. In this case, you would receive a credit for the tax you pay to New York while living in another state. However, in this case, it seems like you are only paying tax to New York on this income. And, unless you are able to itemize deductions on your Federal Return (where you would claim these taxes as a deduction), there isn't another area I can think of where you might receive a credit or a deduction for these taxes.
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