Sounds like a .38 Hand Ejector, Military & Police, 2nd Model, made 1902-1903.
The US service cartridge was really the .38 Long Colt and S&W was still trying for military orders, so they marked their .38 Specials to show they would shoot the Government round.
That is assuming it really is a Smith & Wesson. There were a lot of Spanish and other European copies.
Can you provide close clear pictures of the gun and all its markings?