(A) If the existence of the father and child relationship is declared or if paternity or a duty of support has been adjudicated under sections 3111.01 to 3111.18 of the Revised Code or under prior law, the obligation of the father may be enforced in the same or other proceedings by the mother, the child, or the public authority that has furnished or may furnish the reasonable expenses of pregnancy, confinement, education, support, or funeral, or by any other person, including a private agency, to the extent that any of them may furnish, has furnished, or is furnishing these expenses. (B) The court may order support payments to be made to the mother, the clerk of the court, or a person or agency designated to administer them for the benefit of the child under the supervision of the court. (C) Willful failure to obey the judgment or order of the court is a civil contempt of the court.