There is a strong likelihood that it does not have one. Serial numbers were not required by law on rifles and shotguns until 1968. If the shotgun is a muzzle loader that uses loose powder and shot, it is considered an antique firearm under Federal law, and is not required to have a serial number.
Impossible to answer without knowing who made it and what it is, i.e, handgun, rifle, or shotgun.
You may have some success at the shotgun world website, (shotgunworld.com) there is a vast network of collectors and shotgun experts there that may be able to help
I believe it was known as the "Black Shadow".
Mine is on left side by site on barrow
what is the age of a .36 cal pedersoli black powder rifle serial number da89669
You must take it to a gunsmith to find out.
10-100 usd
20-300 usd
100 or so
50-100 USD
not likely anyone keeps data on re-pro black powder pistols................
10-100 usd