A good guess is that it would have been some kind of fowler or smoothbore.
Not only were rifles expensive but they only fire one type of projectile, a
round ball.  The smoothbore on the other hand offered two choices, the round
ball and bird shot.  If this is a piece of fiction you would be safe to say
that it was an old military musket left over from the Rev War with the fore
stock cut down.  There are many examples of these kicking around in museums.

Just a few thoughts for you.

R. Miner