Got approved for the american tax credit. But it is not showing in my refund amount.

When you claim American Opportunity credit, Form 8863 separately calculates the refundable and nonrefundable portions, which means you report the amounts in two different sections of your return. For example, if you estimate a $2,000 American Opportunity credit, a maximum of $800 may be reported as a refundable tax credit with the remaining $1,200 reported as a nonrefundable credit. A nonrefundable credit is subtracted from your income tax liability, up to the total amount you owe. But unlike a refundable tax credit, a nonrefundable credit cannot reduce your tax balance beyond zero.

Form 1040 will show nonrefundable part AOC on Line 50  and refundable part on Line 68

Form 1040A will show nonrefundable part AOC on Line 33  and refundable portion on Line 44