Deseret News article says the pepperbox Joseph used in Carthage was rediscovered in 1996 and has been on display since 2015.
Trent Toone, "11 fascinating images of Latter-day Saint artifacts," Deseret News, April 1, 2021, accessed December 7, 2021
But Griffiths and Woodger, professors in the Department of Church History and Doctrine at Brigham Young University, did find a multitude of treasures highlighting the global history of The Church of Jesus Christ of Latter-day Saints.
Their list in “50 Relics of the Restoration” includes scripture, documents, weapons, rare coins, clothing, artwork, handmade items and other precious objects dating from the earliest days of the church to recent history . . .
6. Pepperbox pistol
There is documentation that this Allen & Thurber Grafton-style pepperbox pistol was found in the room when Joseph Smith and others were attacked in the Carthage Jail and Joseph and his brother Hyrum Smith were killed. It was later sent to John Taylor. It is not known when it was donated to the Church History Museum. For many years its location was unknown and it was believed to be stolen. It was rediscovered in 1996 and has been on display in the Church History Museum since 2015.