You are likely considered as a nonresident for your NY state filing. Please continue to read.
As a F-1 visa holder, you are considered as "exempt" (not counting days) for five years starting from the year you first enter the United States. In your situation, you are a nonresident for 2016-2020.
According to the State of New York, if you are a U.S. nonresident alien for federal income tax purposes and are required to file federal Form 1040NR, U.S. Nonresident Alien Income Tax Return, or federal Form 1040NR-EZ, U.S. Income Tax Return for Certain Nonresident Aliens with No Dependents, you may be required to file a New York State nonresident return, Form IT?203. Please see NY nonresident aliens page 49 under U.S. nonresident aliens
As TurboTax does not support any nonresident tax forms, you are advised to contact Sprintax to complete both of your federal and state nonresidency tax filings.