The correct answer is option 1, Mandamus. Mandamus is a writ issued by a court to a public official or lower court commanding them to perform a specific act or duty that they are legally obligated to perform. It is used to prevent an official from taking an action that they are not entitled to take, or to compel them to perform their duties properly.

Option 2, Quo Warranto, is a writ used to challenge the legality of a person or entity holding a public office or position. It is not specifically used to prevent an official from taking an action.

Option 3, Certiorari, is a writ used by a higher court to review the decision of a lower court. It is not used to prevent an action by an official.

Option 4, Habeas Corpus, is a writ used to bring a person who has been unlawfully detained before a court. It is not used to prevent an action by an official.

Therefore, option 1, Mandamus, is the correct answer for preventing an official from taking an action they are not entitled to.