Child attended online summer program with Duke university, can I claim the amount I spent on my taxes?

[MichaelMc · Accepted solution]

You did not provide any indication of the age or educational level of your child. The various federal educational tax benefits, the American Opportunity Tax Credit, the Lifetime Learning Credit, and the Tuition and Fees Deduction, are all limited to providing relief for the costs of post-secondary education.

If your child is an elementary or secondary school student taking an enrichment program, there are no federal tax benefits available for such programs. If a high school student is participating in a dual enrollment program, where college credits are earned while remaining enrolled in their "home" high school, the tuition and fees for the college credits would qualify for the LLC or the tuition and fees deduction.

[Hal_Al]

It's complicated, as TurboTaxMichaelMc's answer indicates.
A simplified answer is: if you got an IRS form 1098-T, from Duke, for the tuition you paid, you are probably eligible for a credit or deduction.
You are unlikely to be eligible for the more generous American Opportunity Tax Credit, as that requires the student to be an enrolled degree candidate.