Under the federal tax code, the custodial parent has the right to claim the child as a dependant in the absence of any other formal agreement. Hence the short answer to your exact question is no he has no right to claim her. On the other hand if you want to be sure that this issue doesn't arise in the future, get to the family court and get a formal custody agreement. Also what are you waiting for, get a support order and make sure he pays it. It isn't for you, it is for his daughter.
You are entitled to claim your claim on your income tax filing as your dependent since you are the primary custodial parent. I would do so and inform him in writing that you did not consent to his claiming your child as his dependent, that he is not entitled to any portion of the child deduction, nor any refund you receive. I would further state in your letter that he should expect the same to apply to future tax years. You are the primary custodial parent as established by the status quo over the last several years, but you shold consult with an attorney, your county probably has a pro bono day each week where you can go to the family division and seek assistance with establishing a custody order and child support order. The parties can agree on the amount and the visitation arrangements. If the parties can't agree then the court will make the determination.
As the custodial parent, you claim your child unless you agree otherwise or unless a court has ordered otherwise. He is not entitled to any of the refund as that was factored into your net monthly income when the support amount was arrived at. Domestic Relations takes into consideration the tax obligations of both parties when arriving at the net monthly income on which to base the support obligation. If for some reason you agreed that he take the tax deduction then his monthly support obligation would actually increase to account for this reduced tax obligation.