In Feb 2021, I did a non-deductible contribution from my checking account to a traditional IRA ($6k for 2020) and, on the same day, requested the broker to do a ROTH IRA backdoor conversion on that full amount ($6k).
My question is will this Roth IRA contribution considered for 2020 or 2021? if it's considered for 2021, does that mean I cannot do a backdoor Roth IRA coversion for 2021 any more?
The answer to your question is neither. A Traditional IRA conversion to a Roth IRA is not considered to be a contribution to the Roth IRA.
Since your non-deductible Traditional IRA contribution was for 2020, you will enter that contribution as part of your 2020 tax return and show that it is non-deductible.
Then, in early 2022 you will receive a Form 1099-R for 2021 that will show the distribution from the Traditional IRA. This Form 1099-R will be included as part of your 2021 tax return and you will indicate that the distribution was converted to a Roth IRA.
Then can I do another $6000 backdoor Roth IRA conversion after April 15, 2021?