Sorry for grammar What Smith and Wesson revolver has the patents May 11 1880 Jan 3 1882 and April 9 1889 The serial number on the firearm is 201530 and the caliber is less than 38 maybe a 32?

Sorry- that only tells us that the revolver was made AFTER April 1899. S&W made NUMEROUS different models, including caliber .32 S&W and caliber .32 Winchester Center Fire (.32 WCF, aka 32-20). Contrary to popular belief, a serial number is not unique to only one gun. You best route may be to take the UNLOADED revolver, and visit a gun show in your area. There will likely be a dealer/ collector that can identify it for you.