I'm +90% sure that is a 'parts gun' that a local smith made for some town militia from Bess 2nd pattern parts. How long is the bbl and what does she weigh?
The sight is a recent addition, and the sling dog on the stock is ... I dunno. Most Bess and Bess Knockoffs had only the barrel and triggerguard attachments.
It looks more like a 'wall gun' than a punt/wildfowl gun. First, all of the original 18th century punt guns were pretty crude affairs, and all of the pics I've seen of the small gauge guns (meaning less than 6 or 4bore) had club butts.
That hooked buttplate has no place in a punt, but is perfect for standing, and firing at angry peasants with hay-forks and grubbing hoes storming the walls. It was not loaded with a ball, but with shot, chopped horseshoe nails, etc.
Have you had it apart and checked to see if any proofmarks are on the barrel? If there are no proofmarks, it sure might be an Indian/Turk/Pakistani effort.
If the breechplug is not rusted-out (and as top-good a condition as that is, I seriously doubt it) it is a shooter!
Depending on barrel length, it might have been used onboard a ship, for repelling Saracens and French pirates.