Vegeta Jr. Jr. was one of the infant-like children that Cell had created as a means to make Gohan snap. Sent to torture and kill the young Saiyan's family and friends along with the rest of his siblings, Vegeta Jr. Jr. immediately targeted his namesake Vegeta who was both horrified and disgusted the existence of such an abomination.
Coming face to face, both Vegetas fought with Vegeta Jr. Jr. coming very close to beating and killing his target. Later, after finally tapping into his suppressed power, Gohan beats and seemingly kills Vegeta Jr. Jr.
Though seemingly destroyed, it was later revealed that Vegeta Jr. Jr. survived his death by reforming from a single cell similar to how his father before him had.
Finding himself alone on the battlefield with no where else to go, Vegeta Jr. Jr. became a nomad travelling the Wastelands, occasionally raiding small villages for supplies, but always making sure to avoid any large cities or towns out of fear of what the Z-Fighters might do if they found out he was still alive.
At some point, after finding his way into a deserted area of the Wastelands, he would meet Vegeta Jr., a fellow survivor who had been left alone and forgotten in the wilderness. Though initially hostile towards each other, the two gradually learned to get along and eventually the two formed a sort of father-son kind of relationship.