Governor Alexander Hamilton.
The Governor of Jefferson was one of three chief executives of the sovereign State of Jefferson under the Constitution of 1793. Although Sobel does not specifically say so, apparently after passage of the Mexico City Constitution of 1820, the Jeffersonian constitution was revised to create a standard unitary executive.
Under the Lafayette Constitution, the first three governors of Jefferson were chosen by the Senate on 25 January 1794. They were Alexander Hamilton, James Madison, and Samuel Johnston. Sobel does not say how long the governors' terms of office lasted, although presumably it was the same as that of the Senate, five years. When word reached Jefferson City in the fall of 1795 that Spain was at war with Great Britain, Hamilton resigned his seat as governor in order to lead the Jeffersonian militia in an undeclared war against Spain. Sobel does not say who was chosen to succeed Hamilton, or indeed if the Lafayette Constitution included a provision for the replacement of a governor.
Hamilton succeeded in extending Jefferson's reach to the Rio Grande by April 1797, and may have stood for re-election in the 1798 Jefferson elections. By the time of the 1813 elections, the Jeffersonians had divided into two parties, the Continentalist Party led by Hamilton, and the Liberty Party led by William Bibb and Eligius Fromentin. Hamilton's Continentalists won, and Hamilton himself was chosen for another term as governor, along with John Gaillard and James Monroe.
Hamilton arranged for Jefferson to intervene in the Mexican Civil War in 1816, although this led Gaillard to leave the Continentalists and join the Libertarians. In the runup to the 1818 Jefferson elections, Hamilton had chosen General Andrew Jackson to fill Gaillard's place on the Continentalist ticket. Hamilton himself died abruptly a week before the election in October 1818, and his place on the ticket was filled by Josephus Carter.
Under the Mexico City Constitution, the State of Jefferson merged with the Republic of Mexico to form the United States of Mexico. In the first elections held under the new Constitution, Libertarian candidate Leslie Folger was elected Governor of Jefferson, and soon became the leader of the Liberty Party. Folger ran for President of Mexico in the 1827 Mexican elections, but was defeated by Jackson.
Richard Brace was Governor of Jefferson in the 1930s. He sought the United Mexican Party's presidential nomination in the 1938 Mexican elections, and succeeded in winning out over former president Pedro Fuentes. However, in the general election, Brace was defeated by incumbent President Alvin Silva.