It depends. Since the course was paid for in 2016, you can use that expense as a qualified education expense for your 2016 tax return as long as the course started within the first 3 months of 2017.
Here is some additional information that you might find helpful
With respect to the American opportunity credit, page 10 of Pub 970 says, "for at
least one academic period beginning (or treated as beginning) in 2016,
the student both: was enrolled in a program that leads to a degree,
certificate, or other recognized educational credential; AND carried at least
one half the normal full-time workload for his/her course of study. The standard for what is half of the normal full time
workload is determined by each eligible educational institution…."
It also says, "For 2016, treat an academic period beginning in the
first 3 months of 2017 as if it began in 2016, if qualified education expenses for the student were paid in 2016 for
that academic period".
Per page 11 of Pub
970, "an academic period includes a
semester, trimester, quarter, or other period of study (such as a summer school
session) as reasonably determined by an educational institution….." https://www.irs.gov/pub/irs-pdf/p970.pdf
With the respect to
the lifetime learning credit and the tuition and fees deduction, you would need to have taken at least one course
during the year. However, you can also claim this credit if your academic
period began in the first 3 months of 2017 and you paid the expenses in 2016.
