The general rule is that you can deduct (or use as the basis for a credit) on your income tax return those qualified educational expenses that you actually paid in that tax year, for attendance at an eligible educational institution during that tax year.
However, there is an exception (to allow for the way colleges actually register students for classes and issue bills) that you can deduct amounts paid in a tax year, for an academic period beginning in the first three months of the next tax year.
In your case, you can deduct the amounts paid in 2016 for you student's Fall semester. You cannot claim on your 2016 tax return the amounts paid in January 2017 for the Spring semester; those will be included on your 2017 tax return.
If you had paid for the Spring semester in December 2016, you could have claimed those amounts on your 2016 tax return.
