My son pays child support for his daughter & has her on his health benefits at work. Her mother has primary physical custody & they share legal custody of the baby, but he does have her 2x a week. Can my son take her out as a dependent on his income tax, since he pays a extremely high amount of support??

The support agreement should cover it. If it does not, the IRS says that the custodial parent gets the deduction.

No, merely paying child support does not give him a right to claim the child. And child support is set by state law, so if it is normally about 15 to 20 percent of his gross plus other money

But if he gets to file is in the child custody agreement, if it is not stated, then he can not