You can prepare and file the amended NYS state return with Turbo Tax. If you already filed your return you will need to wait to see if it was rejected or accepted. If they were rejected you are able to login to your return to fix what you need to fix and fix the errors that caused the rejection and refile the return. If your returns were accepted, then you will need to file an amended return. You should not try to amend your return until the original return it has been fully processed and you have received your refund or your payment has cleared.
Amended returns do not “catch up” to your original return and replace them;
they are processed as two separate returns.
Amended returns have to be printed and filed by mail. It can take the IRS
up to 12 weeks or longer to process them. If you are due a larger refund
than on your original return, your amended return should only show the
difference and you will receive a separate check for it. If you owe money
on your amended return, it will show only the new amount owed, you will have to
mail a check with the return. You can check the status of your amended return
by clicking here: https://www.irs.gov/filing/individuals/amended-returns-form-1040-x-/wheres-my-amended-return-1
Click here for amending instructions: https://ttlc.intuit.com/replies/3288565