Well, it looks like a 5" barrel so either a M27 or it's a special order or been cut down.
Five-screw frame so it is old, maybe pre-war.
It is not a Magnum as the chambers are not counter-bored. So it must be a .38, .44 of some variety, or a .45 bore. The brush is not a .38 so if correct for gun the caliber must be .44 or .45.
Finish is either polished bare steel, nickel, or some other aftermarket finish. Looks a little dull for nickel but could be the photo quality. Assume it can't be stainless given its age. But, hammer and trigger appear to be same color as rest of gun, and nickeled Smiths have blued hammers and triggers.
I would guess that whatever it started out as, it has been extensively modified by having the barrel shortened and being refinished, maybe in a hard chrone of some sort, including the hammer and trigger.
Maybe it's really wild and it started as an M1917 with barrel, hammer, and other parts replaced, adjustable rear sight added and a new finish applied?