Claiming Dependents

My daughter lived with me “the non-custodial parent” 180 nights to my ex’s 185 nights of this year. Her new boyfriend said he is going to claim my daughter and my ex as dependents (they are not legally married in Texas no signed affidavits of common law marriage). Can he claim my daughter when she hasn’t lived with him the whole year and her mother is just a dependent??  If not I would like to challenge his claim and claim my daughter on my own taxes. What can I do? Also, if they lie about the marriage and file joint/married can they claim my daughter that way?