No, he cannot. The only way he would get out of supporting his child is if there is a stepfather in the picture who wants to adopt the child.
If the mother isn't following the court order regarding parenting time, then the father needs to consult with an attorney to see how he can enforce it.
If the mother isn't following the court order regarding parenting time, then the father needs to consult with an attorney to see how he can enforce it.