The amount used for claiming education are qualified education expenses you actually paid to the school in 2023 which should be shown in box 1 of form 1098-T.
If your box 1 does not show the correct amount paid, when filling out your form 1098-T in TurboTax, just enter the amount in box 1 of your form 1098-T on the entry screen.
Under box 1, on the 1098-T screen is a radio button: This is not what (student name) paid to this school. Click on that and you will be given a chance to enter what was actually paid in 2023.
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If you didn’t get a 1098-T the school might not be an eligible education institution so you would not be able to claim education credit. The school can tell you if it is an eligible institution and you can check this data base.
I paid for a course that is not listed on the database you gave me, but ultimately received credit from my university for that course. The course was: Homepage - Washington Campus (washcampus.edu). I did not receive a 1098-T from this institution.
If it is not in the data base and/or the school can’t confirm that it is an eligible education institution for the credit, you can’t claim that credit.