Supica & Nahaus list the 1899 as being available in .38 Long Colt, .32-20, and .38 Special.
Jinks confirms that, or at least seems to...
"The introduction of the .38 Military & Police occurred in 1899 and was referred to as the Model of 1899. It was produced in two calibers, the .32 Winchester center fire (.32/20) and the .38 S&W Special."
Obviously, Jinks errs in not mentioning the .38 Long Colt, but it was definitely available in .38 Colt -- the United States Navy took 1,000, and the Army took 1,000 a year later.
I've seen two 1899s marked as being specifically for the .38 Spl. cartridge, and both well within the 1899s serial number range.
As for the .38 Short Colt casing, I don't think I've ever seen one by Remington, so I can't answer that question...