Needing some assistance

I have sole legal and so physical custody of my child, since date of birth. I always filed for my child. Father has now filed also so my filing was rejected even though he has no custody. I mailed in my tax form with my custody paper showing I have sole custody since 2018 and also my new updated support order from 2020. The judge states that I continue to claim the child on my support order. Father has not lived in the same household in years. I'm not sure if he's using my address to file but nothing has come here for taxes. I did file for fraud sometime last year because his stimulus check came here and I sent it back to irs. My question is, if that's enough information to prove that I'm the custodial parent, if not what is? My child has never spent even one night at fathers residence. So the questions he answered to file for a dependent, is fraudulent. My other question is, how can you show proof if he says the child has spent numerous nights with him which is false, but what will they make you show as proof?