Jag
Also: Cleaning Jag
A pointed or ribbed tip that threads onto a cleaning rod and impales or grips a patch to push solvent and fouling through the bore.
A jag is the small caliber-specific tip that screws onto the end of a cleaning-rod and carries a patch down the bore. Pointed jags pierce the center of a cleaning-patch so it wraps tightly and seals against the rifling, while loop or button jags hold the patch differently. The snug fit is what lets the patch wipe the bore surface instead of sliding past it.
Sized to caliber, the jag presses the patch firmly enough to spread bore-solvent evenly and then carry loosened residue back out, which is how a clean patch tells you the bore is getting close to clean. Many shooters keep separate jags for wet solvent passes and dry patches, and most run the patch one direction only, breech to muzzle, which keeps copper-fouling and grit from dragging back across the crown.