You say he is not your dependent. Why not? Is he the other parent's dependent? Most college age students still qualify as their parent's dependent and are not generally eligible for the tuition credits.
A full time unmarried student, under age 24, even if you don't qualify as a dependent, is only eligible for the refundable portion of the American Opportunity Credit if he supports himself by working. You cannot be supporting yourself on parental support, 529 plans or student loans & grants. It is usually best if the parent claims that credit.
You cannot claim a credit if you are, or can be, claimed as a dependent by someone else.
Reference: Line 7 instructions for form 8863. https://www.irs.gov/instructions/i8863
