Is there a law saying if you have your child 15 days out of the month you don't have to pay child support?

Not really. The Child Support Guidelines set forth suggested support figures and contribution percentages that reflect what a child would have enjoyed had the marriage or union remained intact. The number of DAYS you have your child isn't as important as the number of over nights. Normally the noncustodial parent gets a credit for the number of overnights the child has. If, however, the number is equal, you can have support dramatically reduced by applying some recent case law.