My son was incarcerated for part of the year. We paid for commissary items but not for basic living or food expenses. Is he still considered a dependent?

If he was incarcerated more than half of the year, no, you will not be able to claim him.

If your child lived with you for more than half the year and did not provide more than half of their own financial support, then you may be eligible to claim them as a dependent under the qualifying rules.  This article will help you decide if you can claim your son as a dependent.