The tax return you just filed would be for 2019.  No one will be filing a 2020 tax return until 2020 is over on December 31, 2020.  Tax returns for 2020 will be prepared and filed in early 2021.  Go on the NY site and enter the amount you are paying.  If you do not know how much you owe, then look at your state return.

https://ttlc.intuit.com/community/prior-year-return/help/how-do-i-get-a-copy-of-a-return-i-filed-thi...

Thank you so much, this helped tremendously. It was my first time filing. Do you know where I can find information on when the state taxes that I owe are due? I am expecting a federal refund. I would want to wait until that comes to pay my state taxes.