The hat is probably from the 2nd Vicksburg:
The second USS VICKSBURG (Gunboat NR11) was laid down in March, 1896 at Bath, ME, by Bath Iron Works, and launched on December 5, 1896. She was placed into commission at the Portsmouth Navy Yard in New Hampshire on October 23, 1887. VICKSBURG stood out of Chesapeake Bay on April 26, 1898 to join Rear Admiral William T. Sampson’s North Atlantic Fleet in blockading the Northern coast of Cuba during the start of the Spanish-American War. During her patrolling, VICKSBURG captured three blockade runners and came under fire from Cuban shore batteries. Returning to Boston, MA in May, 1899, VICKSBURG was decommissioned. Recommissioned for duty during the Philippine Insurrection in May 1900, she remained in the Far East until 1904. Renamed ALEXANDER HAMILTON, she became a Coast Guard training ship in 1922, and was decommissioned and scrapped on March 28, 1946.