In any case in which counsel other than a public defender has been appointed by the Supreme Court or by a court of appeal to represent a party to any appeal or proceeding, such counsel shall receive a reasonable sum for compensation and necessary expenses, the amount of which shall be determined by the court and paid from any funds appropriated to the Judicial Council for that purpose. Claim for the payment of such compensation and expenses shall be made on a form prescribed by the Judicial Council and presented by counsel to the clerk of the appointing court. After the court has made its order fixing the amount to be paid the clerk shall transmit a copy of the order to the State Controller who shall draw his warrant in payment thereof and transmit it to the payee.