1098-T & Graduate School dependent child

If she is your dependent, you claim her and you enter her 1098-T.

Even if they are her loans, if you supplied more than half her support, you claim her and the expenses paid. 

If you already claimed the American Opportunity Tax Credit 4 times, that credit is no longer available to you.  

If the student was a grad student all of 2021, you are no longer able to claim the American Opportunity Tax Credit. 

HOWEVER, if the student was an undergrad student for any of 2021, and you did not use that credit 4 times, you can apply for it for 2021. You would answer NO to her completing the first four years before 01/01/2021 and enter all expenses, including expenses for Grad school. All education expenses for 2021 would count towards a credit in this situation. 

If there is a state credit, you may need to separate the expenses between undergrad and graduate studies depending on the state. 

IRS Pub 970 

She is your dependent so you should use the 1098-T for Lifetime Learning Credit. It doesn’t matter who actually paid the tuition. Since she has no income she doesn’t have to file a return. I assume she has no scholarship income on that form.