I'm sticking to my guns
that this cannon fragment is from a Colonial-Era Military Field cannon. First... noting that we have somewhat less than half of the barrel's diameter, I estimate from the photo that this cannon's thickness just AFT of the much wider muzzle-swell is at least 6 inches, with a bore diameter of slightly over 2 inches (being a 1-Pounder caliber cannon). Being so thick (6-inches) at the muzzle end (which is typically somewhat smaller than the breech end), that is one honkin' heavy-bodied cannon barrel. No "signal gun" nor swivel gun nor lawn-ornament cannon I've ever seen is so heavy-bodied for its caliber (bore diameter).
In the Colonial Era, ironcasting of very large objects (weighing hundreds of pounds) was still a very inexact, crude science. Large cast-iron cannons typically contained large casting-flaw airbubbles inside the iron, which caused weakness when the iron was subjected to the massive blast of firing the heavy iron cannonball. That is why bronze was preferred over iron for cannons in the Colonial Era. Military shipwrecks from that time typically contain mostly bronze cannons. To compensate for the known weakness of cast-iron, cannons made from that metal were deliberately cast with an extra-thick body in comparison to bronze cannons of the same caliber.
Advances in the science of heavy metal casting in the early 1800s allowed cannons to be manufactured lighter than their heavy ancestors. This is why the famous 12-Pounder Napoleon cannon of American civil war fame was classified as a "Light 12-Pounder."
About trying to match up the muzzle-swell, fillets, etc... good luck.
I will be enormously impressed if anybody can manage to do that. The Colonial Era saw many wars in Europe, and Naval battles in the Caribbean, etc. The Colonial Powers (Britain, France, Spain, even the Netherlands and Denmark) frequently captured cannons from their enemies, and shipped the surplus to their colonies in the Americas. For example, Joe Hunter's cannon fragment could have been captured during the French-&-Indian War, and used by the Americans in the Revolution. It could be a leftover from when New York was a Dutch colony. There is such a staggering variety of European-made (and, Colonist-made) cannons used in the Americas in the Colonial Era, somebody will have to be either extremely skillful or extremely lucky to find a match for this cannon, especially having only the muzzle area to go by. If y'all want to try, I suggest looking for 1-Pounder Colonial Era cannons, European and American. If somebody succeeds, I will publically sing your praises in this forum.
Because I've written so much since my first point, let me repeat it... this cannon, being at least 6-inches thick at the muzzle NOT counting the muzzle swell, in my opinion is too heavy-bodied to be a signal gun, or swivel/rail gun, or lawn-ornament cannon. Cannons which were made to only fire "blanks" (signal guns, lawn-ornament cannons) did not need to be so thick-bodied. Swivel/rail guns were lightweight so they could be mounted on an iron "pin" in the ship's wooden railing.
