Section 461 - Duty to support child after separation agreement, separation, or termination of marriage(a) A separation agreement, a decree of separation, and a final decree or judgment terminating a marriage relationship does not eliminate or diminish either parent's duty to support a child of the marriage under section four hundred thirteen of this article. In the absence of an order of the supreme court or of another court of competent jurisdiction requiring support of the child, the family court may entertain a petition and make an order for its support.(b) If an order of the supreme court or of another court of competent jurisdiction requires support of the child, the family court may: (i) entertain an application to enforce the order requiring support; or(ii) entertain an application to modify such order as provided under subdivision two of section four hundred fifty-one of this article, unless the order of the supreme court provides that the supreme court retains exclusive jurisdiction to enforce or modify the order.(c) In an action for divorce, separation or annulment in the supreme court, the supreme court on its own motion or on motion of one of the parties may refer an application for temporary or permanent support or both of a child of the marriage to the family court. If the supreme court so refers the application, the family court shall have jurisdiction to determine the application with the same powers possessed by the supreme court and the family court's disposition of the application shall be an order of the family court appealable only under article eleven of this act.N.Y. Family Court Law § 461