Within 20 days after the rendering of judgment or other determination of any cause or action in the Supreme Court, Superior Court, or Court of Chancery, the clerk, prothonotary, or register of the court shall enter upon the docket of such cause, action, or prosecution, or in a separate fee book kept for that purpose, a full bill of the costs therein, setting forth distinctly each item of the fees of every officer and person, so far as the same are known to him or her or he or she has in his or her office the means of ascertaining the same.