It is a "replica" of a percussion, or "cap lock" rifle. Real rifles of that general type were made and used from roughly 1830 to after the Civil War. The show was set in modern Alaska, so a real gun of the type would not have a historical connection to the state, having been pretty much obsolete at the time Alaska was purchased from Russia.
A set decorator, pure and simple; intended to give a "frontier" look to the room.
Jim
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