I received UI last year but didn't pay taxes until filling. But I had to repay back the full amount this year. When I enter this amount it does NOT give me back the taxes

[MayaD]

If you are repaying more than $3,000 you have the option of either taking a miscellaneous itemized deduction or claiming a tax credit. If you are taking the deduction but your are not itemizing because your standard deduction is more than your itemized deduction, the repayment won't effect your refund/Tax due.

If you want to claim a tax credit instead of a deduction, you’ll need the CD/Desktop version and will have to calculate the credit manually. Please check IRS Pub 525

Make sure you report the amount you repaid in the year that you actually paid it. 

If you are saying that you repaid back the full amount this year then you will claim it on your 2021 return.

[alek2tl]

But when I do it for the following year. And say I repaid the tax the following year. TurboTax does not update giving back all that tax that I paid.

[ThomasM125]

There are two ways you can get credit for the money you paid back. You can deduct the payback amount as an itemized deduction if the payback amount was under $3,000. The other option is to go back to the year that you received the unemployment and recalculate your tax for that year as if you not received the unemployment, then take a credit for the difference in tax for that year on your current year tax return.

Here is more about how it works, from IRS publication: