Under the special rules for children of divorced or separated parents, the only parent who can claim the child as a dependent is the parent where the child lived more than half the nights of the year. This is the custodial parent under the tax law, and the IRS only counts where the child lived; there is no 50/50 custody, you have to actually count nights. The non-custodial parent can only claim the child as a dependent if they custodial parent gives them a signed form 8332 release form. Even then, the custodial parent can still use the child to qualify for the daycare credit, EIC and head of household status, because those benefits can't be waived, shared or transferred.
So, I assume from your question that you are the custodial parent and you gave the other parent a signed form 8332 releasing the dependent claim. In Turbotax, you should indicate you had custody more than half the year and that you did give the other parent a form 8332.
If you are still rejected after that, it means the other parent filed incorrectly and claimed that the child lived with them more than half the year. You will need to file your return by mail. If the other parent doesn't file an amended return to change their answers, the IRS will investigate.
(The non-custodial parent should have answered they had custody less than half the year and were claiming the child with form 8332. They would then be required to mail the form 8332 to the IRS after e-filing. If they did this correctly, it would not have caused a conflict with your return. If you did not give the other parent a form 8332, you need to do that now.)
All these rules are contained here,
https://www.irs.gov/pub/irs-pdf/p501.pdf
