No, you don't say what amount of tax you want refunded from where.
You would file a New York return and if too much in state tax was withheld, you'll get the excess refunded.
All the state tax paid is lumped into one amount, you don't separate what was withheld from a 1099 from what is withheld from something else, like a W-2.
Your state tax liability is calculated on all your income.
Your state refund is the tax withheld, less your tax liability.
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