Paying for child support has very little to do with who has "custody." To start with, you need to sit down with a family law attorney. Next, you need to file a petitioner for Allocation of Parental Responsibilities. The issue is that who gets what for parenting time and decision making responsibilities is a very fact specific issue and is also dictated by the courts as much as it is the information you present.
Nothing in this communication should be considered legal advice. Nor should this communication lead you to believe that an attorney-client relationship has been created. Only after thorough analysis of your case with you in my office can I provide effective legal advice on your specific issue.