As a ghost, he wields the candlestick he used to carve the numbers into his chest before his death.
Jasper was killed by Walter Sullivan through immolation, so his ghost is still on fire. The body itself is charred and there are visible embers that shift around, particularly on his face during the close-up in his introduction cutscene. The fire seems to mostly come from the upper body, and while the pants and shoes are somewhat burnt, they're mostly intact.
The fire that burns Jasper's ghost may have something to do with his ghostly aura, the same that other ghosts have when attacking Henry, since it diminishes when he's stunned enough or pinned with a Sword of Obedience.
Possibly due to his death by immolation and the fire still burning him, he deals a large amount of damage to Henry with each attack, and can be dangerous if not dealt with. Jasper uses the candlestick to essentially beat Henry using only melee attacks, although he will sometimes attempt to grapple him. Using a Saint Medallion is preferable to dealing with him, as his aura is too strong in itself, and it is strongly recommended that Jasper be pinned in the Forest World as to not show up again later and cause further hindrance to the player.