For mailing a New York State tax return with a debit payment, TurboTax instructions say to use this address:
State Processing Center, P.O. Box 15555, Albany, NY [removed].
However, New York State's own filing instructions say only mailed returns enclosing check or money order payments should go to that address. In contrast, they say tax returns not enclosing a check or money order should be mailed to:
State Processing Center, P.O. Box 61000, Albany, NY [removed].
Just to be sure, which is the right address for a return with a debit payment?
I would mail your NY paper tax return without a check to the PO Box 61000 address. The IRS and some states use a bank lockbox to process tax receipts. So the 15555 address may be a bank lockbox address. TurboTax probably doesn't know or not programmed that you are using ACH debit to pay your balance due.
Here's the from IRS on their lockbox program. I can't say for sure that's what NYS is doing. But I would follow the NYS instructions.