There are a lot of possibilities discussed in the thread, but the user whose handle is GuillibleCynic suggested that with the theme of acceptance on display in the Star Trek media, it would be reasonable to see an Augment on the crew of the Enterprise during the Star Trek: The Next Generation period. After all, the Enterprise had Worf, a Klingon despite being an adopted Federation citizen, so an Augment wouldn't be too weird.
I figured that had Khan's colony survived and regained space travel (a realistic possibility, given how the Augments have lifespans of centuries and Khan has memorized the Original Series Enterprise's technical manuals and has Lt. Marla McGivers to assist him), they might petition for membership in the Federation someday. As long as Ceti Alpha V remains an official or unofficial dictatorship of Khan or a successor (be it a child of Khan and McGivers or his lieutenant Joachim), that isn't going to happen, plus the Federation's psychotic Luddism as far as genetic engineering of humans is concerned isn't helping either. However, for realpolitik reasons, I could imagine Ceti Alpha V becoming a Federation protectorate or being placed under some kind of formal Starfleet quarantine to keep Khan groupies (or people who want to kill him because there's no statute of limitations on war crimes) and aspiring Augmentation enthusiasts from visiting or hostile aliens like the Romulans (or Ferengi, who might like the idea of selling Augment slaves) from messing around.
Although Worf and B'Elanna Torres are Federation citizens, the U.S. military allows non-citizens to serve. The son of the Shah of Iran underwent U.S. Air Force training (and when his father abdicated, made a claim to the throne himself), while many aliens serving in the military were formally given citizenship while serving in Iraq. Allowing an Augment to serve might be good PR about how accepting the Federation is, plus said Augment could serve as a hostage for the good behavior of the Ceti Alpha V government if he or she is well-connected.
So here's my challenge for you. Write a Star Trek: TNG (or Star Trek: Deep Space Nine or Star Trek Voyager since they take place at the same time) fan-fic featuring a surviving Khanate colony sending its sons or daughters to serve in Starfleet. They would be very effective no doubt, but they would also face prejudice from their brothers (or sisters) at arms and have the whole "superior abilities breed superior ambition" (or as Star Trek: Enterprise put it, inborn aggressive tendencies) flaw to face.
Here's a more specific idea I had. The snippet of the Khan novel To Reign in Hell I read online depicts McGivers not becoming pregnant despite years of marriage to Khan and Khan, rather than cheating on her as she feared, instead grooms Joachim as his successor. If you handwave that situation as being caused by stress from the planet's environmental problems rather than her simply being sterile (or having some other reproductive problem the Augments' limited technology can't fix), this Augment original character could be a child or grandchild of Khan himself. I would imagine "Ensign Singh" would face even more suspicion, especially aboard the successor to the ship that their mother or grandmother betrayed to a war criminal. Plus they might harbor fears that history could repeat itself and they could betray their fellow crew. If you want to center a story around this, have him or her get captured by an enemy like the Romulans, who know their history and send in an attractive Romulan as the carrot to the tortuous stick during interrogation.
Good luck, and keep me posted.