Can I request IRS for refund if I believe there was an error of my tax estimation?

not quite sure what you're asking about but if your think you've overpaid your 2021 taxes, there's no way to get it back until you file your 2021 return.

I assume you are referring to quarterly estimated taxes you paid. If you overpaid, that's not a bad thing. But you don't get the over payment refunded to you until you file your tax return for whatever tax year you may be referring to.