Hi,
It looks to be an early 1793 India pattern Brown Bess musket cut back at some later date. It predates the India pattern guns in which the lock markings were stamped rather than engraved. Students of British muskets don't refer to models any more. That was something collectors applied during the late 19th century and 1st, 2nd, and 3rd model Brown Besses gloss over a lot of changes and differences within each model. Moreover, British ordnance never referred to models of King's muskets. It is not a rifle, rather a smooth bored musket more akin to a shot gun. Any provenance it may have to America is either from the War of 1812 or perhaps it was issued to some Canadian troops or militia during the 19th century. Thanks for posting the pictures.
dave