It’s important to understand that a stepparent has the same legal right to claim a child as a dependent as a biological parent, and this relationship does not end with divorce, according to the tax code. Your ex will always be your daughters stepparent according to the tax code and will always have certain legal rights to claim her as a dependent.
The other half of your statement, that your daughter did not live with your ex for at least half the year, would certainly preclude your ex from claiming the child as a dependent using most of the normal rules. But your statement that she is not “his“ anymore does not have any basis in the tax code.
