Can I file an educational tax credit claim on my taxes without a 1098T? My tuition payments went through for 2022 on January 9th 2023, my college says I can still file it

 No.  You can only use payments paid in 2022.  The American opportunity credit is based on adjusted qualified education expenses you pay for yourself, your spouse, or a dependent you claim on your tax return. 

Generally, the credit is allowed for adjusted qualified education expenses paid in 2022 for an academic period beginning in 2022 or beginning in the first 3 months of 2023. For example, if you paid $1,500 in December 2022 for qualified tuition for the spring 2023 semester beginning January 2023, you can use that $1,500 in figuring your 2022 credit.

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Technically, you do not qualify for a 2022 education tax credit, because you made no qualified payments in 2022.