@krystaljean20 said "Since 2018 filing year, my ex and I have each claimed one child".
You are allowed to agree to do that. But, your ex is not allowed to claim "full" tax benefits, sine the child did not live with him for more than half the year. In particular the non-custodial parent can never claim the Earned Income Credit, Head of Household filing status or the day care credit, based on that child, even when the custodial parent has agreed to allowed him to claim the dependency and child tax credit. You can claim those items, even though the ex is claiming the dependent.
The custodial parent has first priority on claiming the children on her taxes; regardless of the amount of support provided by the non-custodial parent. The IRS goes by physical custody, not legal custody. The non-custodial parent can only claim the child as a dependent if the custodial parent gives permission (on form 8332) or if it's spelled out in a pre 2009 divorce decree. Even if a divorce decree, dated after 2008, gives the non-custodial parent the right to claim the child, he must still get form 8332 from the custodial parent. A properly worded decree should require her to provide that form. https://www.irs.gov/pub/irs-pdf/f8332.pdf
