Final answer:
William Marbury, a Midnight Judge appointed by John Adams, sued James Madison for the delivery of his commission, leading to the landmark Marbury v. Madison case which established the principle of judicial review.
Step-by-step explanation:
The name of the Midnight Judge who sued James Madison was William Marbury. He was appointed by President John Adams as a Justice of the Peace for the District of Columbia, but his commission was not delivered before Adams left office.
When Thomas Jefferson became president, he instructed his Secretary of State, James Madison, not to deliver Marbury's commission. In response, Marbury sued for his commission by petitioning the Supreme Court for a writ of mandamus based on the Judiciary Act of 1789.
The resulting case, Marbury v. Madison, decided by Chief Justice John Marshall in 1803, ultimately led to the principle of judicial review, establishing the Supreme Court's power to declare acts of Congress unconstitutional, despite ruling that the court did not have the power to compel Madison to deliver the commission.