E-filing is permanently closed for 2021 returns. And...you can mail your NY return.
New York prefers e-filed returns, but there are certain circumstances that make it necessary for you to file your NY return by mail and the state DOES allow mailed returns. If you could not or did not e-file your federal return then your NY return cannot be e-filed. It has to be mailed. It is not possible to e-file any state return if the federal return was not e-filed and accepted by the IRS.
https://www.tax.ny.gov/pit/efile/efile_mandate_for_individuals.htm
https://www.tax.ny.gov/pit/file/return_assembly_mail.htm
You must pay your state tax due using the state’s preferred method of receiving payment. For most states that will be by making a payment to the state’s own tax website, or by mailing a check or money order.
https://ttlc.intuit.com/turbotax-support/en-us/help-article/state-taxes/contact-state-department-rev...
**Disclaimer: Every effort has been made to offer the most correct information possible. The poster disclaims any legal responsibility for the accuracy of the information that is contained in this post.**