No, you cannot deduct tuition paid to the high school for taking the AP classes or the fees paid for the tests.
Per IRS, if your child is still in high school but takes classes at or through a college, university or trade school, you may qualify to write off those tuition costs as part of the tuition and fees tax deduction or the Lifetime Learning Credit. For example, if your child enrolls in a biology course at the local college as part of an early-entry program while he's still in high school, you could use the tuition that you pay to the college for the deduction. The deduction is limited to $4,000 per year.
However, the deduction does not include costs paid to the student's high school or for special tests, such as Advanced Placement or International Baccalaureate tests, because those costs are not paid to a qualifying educational institution. You also can't deduct the portion of the high school tuition that goes towards the AP or IB classes. Qualifying educational institutions are only those that can participate in financial aid programs sponsored by the U.S. Department of Education, which include colleges, universities and trade schools, but not high schools. Finally, you can't claim the deduction if you don't claim your child as your dependent.