I have full custody the ex is not in the relationship at all. how can she claim custody.she has no custody rights

If your "ex" claims the child ----and should not be able to---and she files first, your own e-file will be rejected.   If that happens, then you will need to go ahead and claim the child but file by mail.  Then the IRS will sort out the conflict.   She will be subject to repaying any child-related credit she received if she should not have claimed the child, and perhaps some penalties as well.

Are you the custodial parent?  Do you have an agreement with the other parent to allow the other parent to claim them--due to divorce or that you live apart and share custody?  Did one of you sign a Form 8332?

If there is a signed 8332 then the custodial parent retains the right to file as Head of Household, get earned income credit and the childcare credit.  The non-custodial parent gets the child tax credit for children under the age of 17.

As far as the IRS is concerned, the custodial parent is the one with whom the child spent the most nights during the tax year--at least 183 nights.