What counts as a year towards the American Opportunity Credit?

My Son graduated from high school in May 2016. The previous summer (June 2015) he took a college course online as part of a dual enrollment program where he got credit towards in high school diploma. The college that sponsored his online class sent me a 1098T for cost of the online course and I entered it into TurboTax for my 2015 tax return. This year he is a full time freshman college student at a different university. Did I burn a year of the American Opportunity Credit when I claimed his online class in 2015?

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Yes. As you have discovered, the AOTC is only for 4 years even though students typically attend undergraduate school for 5 calendar years. You could file an amended 2015 return and remove the tax credit, but keep in mind that the credit maxes out at $2500, and that when he is a senior, you could still qualify for the Lifetime Learning Credit or the Tuition and Fees deduction.