I'm a student and I paid my school fee for 2020 in January of 2021. can I claim my education credit now?

No, you can only claim education expenses paid in 2020.

But, if you paid the education expenses in 2020 for the first three months of the following year (2021) then you can include this on your 2020 tax return. Usually, this amount is included on your 1098-T in box 1 when box 7 is checked. If it isn't included on your 1098-T then please follow these steps:

1. Login to your TurboTax Account 
2. Click on the Search box on the top and type “1098T”
3. Click on “Jump to 1098T”
4. Click the link "This is not what I paid to this school" under box 1 on the 1098-T screen and enter the proper amount in the box on the right that will appear. 

[Edited 2/14/2021 | 1:44pm PST]

@fm1934 

@DanaB27  said "Yes, if you paid the education expenses in 2020 for the first three months of the following year (2021) then you can include this on your 2020 tax return."

 

That is correct, but that doesn't sound like what you did.

 

Q.  I paid my school fee for 2020 in January of 2021. Can I claim my education credit now (on my 2020 tax return)?

A.  No.  You must pay  for the expenses in the year they occurred (see DanaB27's comment for the exception) to qualify.  For you, this is a double whammy.  You will also not be able to count that payment on your 2021 return because it was not a payment for either 2021 or 2022 expenses.