What is the history and value of a Smith and Wesson 38 Special 6 shot revolver with no serial number SN is carved on a leathercase carried on leatherbelt belt also holds the bullets on side of it?

If it doesn't have a serial number, the chances are it was removed. It might have been a case of an overzealous refinish or a purposeful obliteration. I would suggest a very close examination of the butt and crane area to see if perhaps the sn is there, but, struck weakly. There is the chance that it was made that way, but, very remote. You need to contact a lawyer who specializes in fireams.