Who claims the 1098 t form, the student or the parent

Dependents cannot get education credits.  The parent who is claiming the dependent gets the education credit.

Q. Who claims the 1098-T form, the student or the parent?

A. Simple answer: the parent. More accurately, usually the parent. As other have said, if the sytudent is a dependent, then the parent claims the tuition credit. 

 The 1098-T is only an informational document. The numbers on it are not required to be entered onto your tax return. However receipt of a 1098-T frequently means you are either eligible for a tuition credit or possibly your student has taxable scholarship income.  It necessary, the 1098-T could go on both the parent's and student's tax return, with adjustments. 

If you claim the tuition credit, you do need to report that you got one or that you qualify for an exception (the TurboTax interview will handle this)

You claim the tuition credit, or report scholarship income, based on your own financial records, not the 1098-T. In the 1098-T screen, click on the link "What if this is not what I paid the school" underneath box 1. You will then be able to enter the actual amounts paid. You will also reach a screen that allows you to adjust the scholarship amount for "amounts not awarded for 2023 expenses".

Or if you find it easier, just change the numbers in boxes 1& 5 to what your records show. The 1098-T that you enter in TT is not sent to the IRS.