How to claim back prepaid income tax for the period without income

There is no pre-payment of income tax for employed persons.
So I assume during the mentioned period you were self-employed (if not, please explain your status then). In that case, the tax authority asks for payments of tax on estimated or expected turnover and profit. If you have less (or no) income in the end, you will of course get the payments back.
Just state everything correctly in your 2021 tax declaration. Since preparing it is rather complex, especially for self-employed, I recommend engaging a tax consultant for this.
The taxes you actually paid are, of course, already known to the taxmen.

Thanks beppi.  I quit my job and took a break in Q4-2020.  My company must have informed Finanzamt who sent me within a short time a tax prepayment notice for Q4.  I simply settled it since I knew that I will definitely get it back. 
The question I have is how to input such information in the tax return.  I've just found on my tax declaration software a place to provide input about prepaid tax.  It seems not the same as adding up the prepaid tax to the deducted tax during my employment period, but instead a separate entry.

I have never heard of a case where a non-working person has to pre-pay tax and I don't think it is legally correct. Instead, you should have received unemployment benefits during that time!
Are you sure this came from the actual Finanzamt - and not some fraudsters? If in doubt, call and ask! (And then also ask them where to indicate it in the forms!)