If you son worked and paid Federal taxes, he can file his own return to get his tax withholding refunded.
If he lives with you and is your dependent, he can indicate on his return that he is a 'dependent'.
If you shared a Marketplace plan, whoever received a Form 1095-A will enter it in their return, indicating that they 'shared' the policy with the other person, so the insurance does apply to both filings.
Here's some info that may be helpful on Allocating 1095-A and Dependent Filing Requirements.