It's called simply the .44 Double Action, if it is a DA, which I think it is from the patent marking. About 54,668 of them were made, in .44 Russian, catalogued from 1881 to 1913. But it's still an Antique, as all frames were made pre-1899. .44 Russian ammunition is simply a short .44 Special. I don't know if that caliber is made for the Cowboy shooters, but it may be. If not, it can be made up pretty easily by any handloader of .44 Special or .44 Magnum by shortening .44 Special or .44 Magnum brass. But only very light smokeless or black powder loads should be used.