I graduated in May 2019. I received a 1098-T for 2018 that includes payments made for Jan-Mar 2019. How do I claim this?

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You can not claim payments made in 2018, on your 2019 tax return, even if the payments were for the 2019 term.

If you (or your parents, if you were their dependent in 2018) failed to claim that money on your (their) 2018 return, you (or they) can file an amended 2018 return. If you (they) already received the maximum credit, the additional payment will not get you any more refund.