No. You do not include your sons income on your return.
However, if he was on your 1095-A, he will need to include that on his return as well and you will both need to choose that you share the policy with another taxpayer. Then you will be able to allocate an amount to you and your son. You can claim 100% or 0%, he can do the same as long as it adds up to 100%. Many times parents paid the premiums and will allocate the full amount to themselves, while the kids just enter the form and allocate 0%.