If I have full sole and physical custody, is my baby daddy allow to claim our kids on his tax without my permission?

I'm not sure what to do with this. He give me $400 a month for 2 kids. when I asked him to help me pay for their after school program he always say he doesn't have it. basically he feel like he give me 400 and that's it. whenever he decide to not come get them on the weekends I have to pay someone to babysit them for me. since I see he doesn't want to give extra help I make sureni don't ask hikm for anything else. I let him live his life, I don't bother him, I act like he doesn't exist to me. I talk to him because of the kids and because i want the kids to have a bond with him no matter what. and now this man have the nerve to file tax with my kids without consulting me.