When Khan revived his people on the Botany Bay and brought them to the Enterprise with assistance from Lieutenant Marla McGivers, he informed Joaquin that the battle had begun again, only they'd win more than a world. They'd win a universe.
Joaquin was in engineering along with the Augments when Khan began taking control of the Enterprise and threaten to suffocate the crew if Kirk didn't surrender the bridge.
As the Augments held the crew in the briefing room, Joaquin hit Uhura to force her to activate the viewing screen so Khan would force the crew to watch Kirk die in the decompression chamber. Joaquin would've hit her again were it not for McGivers' intervention. When McGivers cut off the channel to the decompression chamber, Joaquin was about to hit Uhura again just to regain picture, but Khan claimed it didn't matter since he was sure the captain was dead, but this was proven wrong as McGivers freed Kirk and ordered Spock to gas all decks but the one they were on and Joaquin ended up unconscious with his fellow Augments while Khan escaped to engineering where Kirk defeated him in combat.
Once Kirk and crew regained control of the Enterprise, Joaquin and the other Augments were sent to Ceti Alpha V along with Khan and McGivers, who opted to go with them rather than be court-martialed for treason. (TOS: "Space Seed")
In Greg Cox' novel To Reign in Hell: The Exile of Khan Noonien Singh, Joaquin's last name was Weiss. He was an Israeli national who was serving a life sentence in an Israeli prison for murder when Khan rescued him from prison. From that point on, he was Khan's faithful bodyguard. Joaquin trusted nobody around Khan and even later, after the exile to Ceti Alpha V, was suspicious of Marla McGivers for a time. This began to ease when she and Khan were married and McGivers ultimately gained Joaquin's unqualified respect when she committed suicide rather than attempt to kill Khan after she was infected with a Ceti eel. At the same time that she and Khan were married, many of the colonists paired off into couples to start families as well. To that end, Joaquin married Suzette Ling and ultimately became the father of Joachim, who was one of Khan's crew in Star Trek II: The Wrath of Khan. Joaquin was killed defending Khan from a rebellious Augment who tried to take over the underground colony on Ceti Alpha V. Because of his and Ling's faithful service to him (she also died fighting for Khan) Khan felt that the least he could do for them was to take their son Joachim and raise him as his own.