For proceedings in probate deposits and fees shall be paid to the Register of Wills.
Upon the presentation for filing of a petition or a caveat to a will, he may require a deposit for his fees to be charged for the proceedings under the petition or caveat. Upon the deposit becoming exhausted in the liquidation of his fees so charged, he may require a further deposit from the original petitioner or caveator. The deposits may not be required in excess of fifteen dollars at any one time.
D.C. Code § 15-708