Does the divorce pronounced in the form: "You are divorced threefold, and forbidden to me until the Day of Judgment, if you do not tell me what sorcery you have done to me," with the intention of threat, take effect, and what is the expiation for this oath?

As long as the wife has denied practicing magic, and there is no conclusive evidence to contradict her statement, then the default is to believe her. Therefore, no divorce or prohibition has occurred, and no expiation is binding on the husband. It is advisable to avoid uttering words of divorce and prohibition as a threat, and it is not permissible to accuse anyone of magic without clear proof.