Assuming you are amending a 2024 Form IT-201-X, you will need to mail your amended return based upon whether you need to mail in a payment or not based upon the form instructions on page 4.
If you owe money with your amended return, you will mail it and Form IT-201-V to: State Processing Center, PO Box 15555, Albany, NY 12212-5555.
If you do not need to include a payment, you will mail the amended return to: State Processing Center, PO Box 61000, Albany, NY 12261-0001.