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Let me better clarify my question.

My Estimated Tax quarterly payment for Q1 is still due tomorrow, 4/15.

I have a large refund from my 2020 taxes, which aren't yet filed.

In order to apply (part of) my 2020 refund to my Q1 estimated payment, do I have to file my 2020 return by 4/15 (when the Q1 Estimated payment is due)?  

Or can I just file my taxes before the new return due date (5/17) and still have that quarterly payment be considered on time?  IRS has actually had the $$ for months already - the refund mostly is the result of overpaying my estimated payments in September and January.