Hello. If the child is not your child, step child (married to child's mother), adopted child, foster child etc, you wouldn't meet the tax law requirement to claim Head of Household for that child. If you had another child that qualified you for that filing status, that would be fine.
Regarding the 1095A, it matters who the primary insurance holder is. If the child's mother is the primary insurance holder, she could reconcile the Premium Tax Credit(PTC) on her return. So if you are claiming the child as a dependent, you will need to indicate the 1095A is reconciled on another return. Let me know if you have more questions.
