Yes, NY taxes its residents' income no matter where they earn it.
They will, however, give you credit (against your NY tax) for any tax you pay to another state on the same income. You will have to prepare the non-resident state return first (if any) to see how much tax you have to pay there.
The computation of your New York State (and New York City and
Yonkers) income tax is based on information you reported on
your federal income tax return, including your income and federal
adjustments to income. If you did not file a federal return, you
must report the same income and adjustments that you would
have reported for federal income tax purposes if you had filed a
federal return. There are no adjustments for income earned elsewhere, but there is a credit for taxes paid to other jurisdictions.
