A non-Federation world to which Richard and Amsha Bashir took their young son Julian for illegal genetic resequencing, as revealed in Doctor Bashir, I Presume.
Adigeon Prime lies outside the reach of Federation law, which has banned the genetic engineering of humans since the Eugenics Wars. In Doctor Bashir, I Presume, Julian Bashir admits to O'Brien that his parents took him to a hospital there shortly before his seventh birthday.
As a small child Jules, as he was called, was slow to learn and fell behind his classmates. Over about two months on Adigeon Prime his neural pathways were accelerated, raising his intelligence, his coordination and his stamina. The family then moved and enrolled him in a new school, keeping the treatment secret.
The truth emerges in 2373 when Doctor Lewis Zimmerman interviews Bashir's parents for a holographic medical programme. To save his son's career, Richard Bashir pleads guilty and accepts two years in a minimum-security prison.