The Ansata were a terrorist faction from the planet Rutia IV, hoping to gain independence from the primary Rutian government. They gained renewed vigor in the 2360s from the use of a folded-space transport device known as an inverter, despite its lethal side-effects.
In 2352, the Ansata assassinated a team of Federation diplomats, including Elix Barus. Until that point, Caera Shean was a member of the sect, and had been having an affair with Barus, which ultimately resulted in the birth of their son, Ciaran. (Star Trek: A Call to Duty)
In the year 2366, Ansata leader Kyril Finn kidnapped Starfleet officers Beverly Crusher and Jean-Luc Picard in an effort to gain Federation attention. (TNG: "The High Ground")