Which writ is issued by a court to ask a person holding a public office under what authority he is holding it?

Quo warranto means 'by what authority'. The court issues it to examine the legality of a person's claim to a public office, and to prevent illegal usurpation. Mandamus commands a public official to perform a public duty, certiorari quashes an order already passed by a lower court or tribunal, and prohibition forbids a lower court from exceeding its jurisdiction while proceedings are pending.