Harper's Ferry 1852 lock and patchbox point to a model of 1841, the "Mississippi Rifle." It was produced from 1841 until 1855.
Original caliber was .54, some were rebored to .58 for common ammunition with the 1855 and later rifles and rifle muskets. Others, especially in the South, stayed .54 and they made Minie balls for them.
Show pictures at full length, its desirability depends on its originality. If the barrel and stock have been shortened, its value is much less.
If it was upgraded in service by reboring or adding bayonet lug or better sights, it would be of interest but not much lower or higher in dollar value.
The large P on the stock is not an official government marking, likely the soldier or some owner after it was surplused.