Can i claim my daughter if her father has her on his health insurance through the market place

My daughter lives with me full time. Her father and I were never married and we had an agreement that he will get health insurance and because his job does not offer it he went through the market place. When I file my taxes I claim her cause she is with me all but 20 days out of the year. How will that work if he pays for health insurance and his income is MUCH lower then mine so he gets a high  subsidy.  Am I going to be penalized and have to pay that part back for her part of the insurance when I claim her on my taxes. Or is he going to have to claim her on his when all he pays is the insurance and nothing else for her over the year.