State tax filing
Yes, that is correct. According to NYS, the credit is refundable only if your NY AGI is $60,000 or less. If your NY AGI is greater than $60,000, you can only carry forward the excess credit to future years. Please see the screenshot below from the linked NYS website.
Since the credit is nonrefundable in your tax situation, the carry forward of the credit can only be applied to future NYS tax liability.
