It depends. The expenses count in 2016 if you paid for them in 2016. TurboTax will ask you a question about a 1098-T received in 2015 with amounts billed for 2016, so you can cover this part by entering in your 2015 1098-T showing that the box was checked for amounts billed for 2016.
You will want to be sure that you meet the other qualifications for the American Opportunity Credit. One of those requirements is that you were a half-time student for half of the year (5 months). There are other requirements, as you can see in this FAQ: https://ttlc.intuit.com/replies/5358150
But if you meet all of the other requirements, your amounts paid in 2016 may be claimed for the credit, even though they were reported as billed in 2015.
**Say "Thanks" by clicking the thumb icon in a post
**Mark the post that answers your question by clicking on "Mark as Best Answer"