It's pretty flat - usually indicates a smoothbore, musket or rifled musket. Four screws (rather than a screw or two and pinned tang) would indicate 1820 or later. Screws were hard to make before they were mass-produced. So that takes us past flintlocks into percussion era or cartridge.
The "horns" are decorative - which rules out military musket or rifled musket.
So, that leaves: Shotgun/smoothbore (fowler), trade gun (fancier grade), English style percussion rifle (if made of iron/steel).