Yonada was a multi-generational world ship that was built in 7500 B.C. by a group of Fabrini, when they realized that their home star was about to enter a nova phase and would eventually destroy all life on Fabrina. (Last Unicorn RPG module: All Our Yesterdays: The Time Travel Sourcebook)
This group, known as the Creators would later come to be worshipped as gods by the Fabrini. They constructed Yonada out of a hollowed-out asteroid. Using shaped anti-matter charges they compressed an asteroid into a collapsed matter core and then bombarded it with carbon to build a diamond shell around the core, giving the ship artificial gravity. The Creators then built the ship around the collapsed matter core, and covered it with an asteroidal surface - which was the best method available to them to protect the ship from debris and radiation.
Approximately 60 years after beginning the project the Fabrini finally finished the Yonada and moved the selected population on board the ship. The ship was then launched out of Fabrina orbit, and was able to accelerate out of range of the Fabrini star Ganidra before it went supernova. The ship went on a computer-controlled course to a habitable planet 32 light-years away, in sector 54R's Daran star system, with approximately 40 million Fabrini residing inside the shell. The Federation starship USS Yonada was named for this world.
The journey was not an easy one. Over the centuries the Fabrini had difficulty maintaining Yonada's environment, which led to several violent upheavals. During one of the last of these violent upheavals, a group of religious fundamentalists took control of Yonada, and reprogrammed the Oracle of the People to suit their ideology. Instruments of Obedience were then implanted in all Fabrini. Over the centuries of travel, Yonada's computer, known as the "Oracle", had degraded and the worldship's course altered from an orbital course for Daran IV, to a collision course with Daran V. Meanwhile within a few generations the Fabrini had forgotten that they were on a spaceship and soon developed a religion around the "Oracle" and its mission to find them a new world. (TOS novel: Ex Machina)
In 2268, the USS Enterprise encountered the worldship when it was fired upon by the automated defense systems of the Yonada. A landing party consisting of Captain Kirk, Spock, and Dr. McCoy helped Natira, the leader of the Yonada colonists, to understand that their world was actually a ship, and corrected the worldship's course to its intended destination. (TOS episode & Star Trek 8 novelization: For the World is Hollow and I Have Touched the Sky)
In 2270, Yonada arrived in orbit and the population moved down to establish a colony on Daran IV, with assistance from the Federation. Yonada was kept in orbit of Daran IV, but proved a symbol for some who wished to return to the old ways of worshipping the "Oracle." As part of the peace process, plans were discussed regarding moving Yonada into a higher orbit, but covering it with reflectors or painting it white so that those wishing to worship the ship could still do so. The SCE team in the system also began work to verify the stability of the collapsed matter core and also began working on more modern means of reinforcing the core. (TOS novels: The Lost Years, Ex Machina)