Did the Americans fight the Mexicans at Tucson, Arizona during the Mexican-American War?

Yes, there was a significant battle fought at Tucson, Arizona during the Mexican-American War. The Battle of Tucson took place on August 16-17, 1846. American forces under the command of Lieutenant Colonel Philip St. George Cooke, who was a part of the California Battalion, attacked and captured Tucson from the Mexican garrison stationed there. This battle was a part of the larger campaign to secure the region of present-day Arizona as part of the United States during the Mexican-American War.