Ken is the son of the three-eyed mutant, Triclops, and a Jedi princess called Kendalina. Triclops is the son of Emperor Palpatine, and had been placed in the Imperial asylum on Kessel, where he was to spend the rest of his days. It was here that he met Kendalina, and where they fell in love and conceived a child.
The grandson of Palpatine, Ken, was born. But soon after he entered the galaxy, his mother was killed. After this he was taken to the Lost City of the Jedi on Yavin Four. He did not know who the brown-robed Jedi Master was who secreted him to the City, but once there he was trained to reject is heritage. The Jedi did not want Palpatine's grandson to fall to the Dark Side, for they knew he could be very powerful and dangerous. Therefore he was taught to embrace the Light Side, and his memories of his father and mother faded as time passed. He did, however, have a small reminder of Triclops. It was a half of a silver birth crystal, which was worn around his neck. It turned out that Triclops wore the other half.
At the Lost City, Ken was surrounded by droids. DJ-88 was the Jedi librarian, and was also employed as Ken's teacher; HC-100 was put in charge of Ken's homework; Microchip, aptly named due to its size, was built to be Ken's friend, ad was given the nickname of 'Chip'. He even had a pet; a Mooka called Zeebo.
As his teachings progressed, Ken learned more and more about the war with the Galactic Empire, and soon wanted to meet the heroes of the Alliance. Most of all he wanted to meet Luke, a hero and fellow Jedi. By then Ken had learned to use the Force to levitate small objects and cloud the minds of others, much like Ben had done at Mos Eisley.
During all his time in the Lost City, Ken had been kept in the bowels of the City. But a year after the Battle of Endor, he took Chip and made a daring journey o the surface. By now he was twelve, and extremely curious about what else was happening around him. On the surface he went into the forests, and there he found Luke with a being named Baji, a Ho'Din healer. From his journey Ken had gained much knowledge about where the Lost City was in the galaxy, but before he could tell anyone else its location, DJ-88 took him away, having followed his young student.
At about this time, Kadaan and Trioculus were seeking guidance about a problem they had encountered. Kadaan was the Supreme Prophet of the Dark Side, while Trioculus was planning to take over as Emperor of what remained of the Empire. The Prophet had predicted that a young Jedi prince would emerge and destroy them, and that he was located on Yavin Four. Therefore they went to the fourth of moon of Yavin, with the sole intent of killing Ken. Thanks to Chewie, Han, and Luke, Ken and his droids made sure the Dark Side Prophet and the Emperor-to-be failed in their attempt. Seeing that he was ready, Luke then allowed Ken to leave the City and join the Alliance, and train with the Jedi Master.
During the time that followed, Ken travelled with the Alliance heroes, and was involved in a few of their adventures. But his destiny and heritage would soon step in. His adventures eventually took him to the planet Duro, and the Valley of Royalty. Unbeknownst to Ken, the Imperials were keeping Triclops prisoner there. But the he managed to rewire an assassin droid and use it to escape. It was in the mazelike walls of the Valley that Triclops encountered the Alliance and Ken. He immediately recognised the pendant around Ken's neck, and knew he had at last found his son.
Triclops did not reveal who he was, as he did not want Ken to look back and become like his grandfather. But Kadaan found Ken and gave him a truth serum. It while under the influence of the serum that Ken gave away the location of the Lost City. Afterwards, when they had gone to the City, Kadaan revealed Ken's past to him, hoping to turn him against his friends and fall to the Dark Side. But before much damage could be inflicted on Ken's mind, Luke, also a prisoner, escaped and rescued the young Jedi. He then trapped Kadaan and his troops in the City, which by then had been shut down.
When things had calmed down, Ken went to confront his father, but found that Triclops had fled into the dense jungles. He followed his father, and neither has been seen since.
It is very possible that the son and grandson of Palpatine will re-emerge some day, but whether it will be to claim the throne of the Empire, or to once again join the Alliance, no one knows.