which state’s capital is the only one named after a former vice president of the united states?

The only U.S. state capital named after a former Vice President of the United States is Jefferson City, Missouri. It is named after Thomas Jefferson, who served as the second Vice President of the United States under John Adams from 1797 to 1801 before becoming the third President. Jefferson City was named in honor of Jefferson largely because he was responsible for the Louisiana Purchase, which included the land that became Missouri. This makes Jefferson City unique among U.S. state capitals in being named after a former Vice President.