I paid $4900 to the mother of my child for child support .

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