I received my second stimulus check on Jan 3rd 2021. Should I claim it on 2021 taxes or last years (2020)?

Yes enter the second Stimulus payment on your 2020 return now.  The year you got it doesn't matter.  If you don't report it Turbo Tax will give it to you again, which would be wrong and double.  The Stimulus entry screen says the second one is between Dec 2020 and Jan 2021 so you should include January.

Thanks,  It's sort of unusual report something OUT of the normal tax year.  I'm certain this question may come up again.

Thanks again

Dan