Josephus Carter was a member of the Continentalist Party in the State of Jefferson at the time of Jefferson's intervention in the Mexican Civil War of 1806 - 1817. When Alexander Hamilton died a week before the 1818 Jeffersonian elections, Governor James Monroe chose Carter to take Hamilton's place at the head of the Continentalist Party ticket. Following a sweeping Continentalist victory, Carter took his place as one of the three governors of Jefferson, alongside Monroe and Andrew Jackson, in December 1818. While Jackson controlled domestic policy and relations with the Republic of Mexico, and Monroe dealt with the Confederation of North America and the European nations, Carter handled the administrative details of the Jeffersonian government.
Following Jackson's departure for Mexico City in the spring of 1820, Carter effectively became Jackson's surrogate in Jefferson City. In June 1820, acting on Jackson's behalf, Carter asked the Jeffersonian legislature to call a new constitutional convention in Mexico City. The legislature did so on June 15, voting to dissolve itself and then reconstitute itself as a constitutional convention on September 22. Carter was a member of the Mexico City Convention and helped draft the Mexico City Constitution. Carter's term as Governor of Jefferson ended in September 1821, when a new Jeffersonian government took office under the United States of Mexico. Sobel makes no further mention of Carter, although he probably continued to serve in either Jefferson's government or as a member of Jackson's Cabinet.
Sobel's source for Josephus Carter's career as co-Governor of Jefferson is George Tinker's The Monroe-Jackson-Carter Administration (New York, 1967).