The founder of the clan was a German-British man in Manchester whose three children were all ESPs, himself included. And his grandchildren were all ESPs as well, and that was how the Klisis clan began.
According to Earth archive, the name of the German-British man was Hildebrant Fashingbauer who lived until 321 years old and died on year 4944. He was the founder of the Klisis clan after seeing his children as well as grandchildren were all ESPs.
Fashingbauer was an illegal last name as last name system was demolished. Self-claimed last name still existed.
The Klisis clan had always been a defensive clan due to their small numbers. And the family eventually developed their own skill to combat outnumbered situations.
“The spiritual blades”, also known as “Imaginary blades”, summoned seven swords that floated around its caster. It required many years of dedicated training to be able to manipulate seven blades simultaneously.
Reflecting the skill, the family crest had seven blades protecting their family shield which bore a unicorn, indirectly symbolizing that the clan was shrouded in mystery and protection.
The Klisis clan had surreally high rate of newborns becoming an ESP. Over 90% of their members were ESPs and over half of them were class A. What that meant was that, even though the clan number never exceeded a thousand even in its prime, their realistic raw firepower was immense. And the Klisis ESPs were highly disciplined and trained who were simply better in every aspects.
Thus, it was hardly a secret that the Bau desired the Klisis. The Bau made numerous attempts to either vassalize or absorb the clan for thousands years. The Klisis clan defensed by shutting themselves down in Manchester, England. Unless must, the clan members refused to venture too far from their own clan stronghold. Schooling was done within the clan and so did marriages.
Yes, inbreeding was common within the clan because they believed it was necessary for them to maintain the high rate of ESP birth. Medical technologies were advanced enough to cure almost all birth defects.
Whether coincidence or not, their inbreeding culture seemed to have a positive effects on quality of ESP and the clan was the first one ever to produce a class S ESP which the Bau referred as “A human treasure a clan must have”.
Indeed, a presence of a class S ESP within the clan meant they could stay independent easily. The clan was famed for having at least one class S ESP in every two generations at least. And in Cecil’s generation, they had class S ESPs for two concessive generations.
Cecil Klisis, the most fearsome ESP known to mankind, was in charge of the clan when he made a dire decision to relocate the clan to Venus. His decision was based on a fact that their next generation had no class S ESP and he feared the Bau would finally succeed in their attempt to absorb the clan when he was gone.
The Bau would normally reject their relocation and would prevent them from leaving Earth but the Bau was very unstable at the time and the situation was in Cecil’s favor.
Their relocation is covered well in a story: [Cecil arc]  [To Venus] 
A small clan, the Vues, benefited from their location and also relocated to Venus on the same year.
The fall of the Klisis was largely due to Cecil’s importance in the clan. He was simply too important for the clan to function without him. When Cecil chose to work with President Mirren, he was forced to leave the clan in his younger brother’s, Konrad, hands who unfortunately wasn’t qualified enough to lead the clan. The O’ren made numerous attempts to absorb the clan when Konrad was in his seat and eventually Konrad chose the unthinkable, killing the O’ren diplomats which resulted the O’ren to attack and annihilate the clan.
In O’ren defense, they had the right to and did pay a heavy price when Cecil massacred their HQ and killed few millions.
Cecil adopted Gair and raised him as a leader. When he took over Venus, Gair was appointed to be the vice President and handled most of diplomatic matters in his seat.
When Cecil eventually left Venus, he left Gair in total control and asked him to resume the Klisis clan once more. Gair accepted, thus becoming Gair Klisis. He was also taught the clan’s traditional spiritual blades skill in early age as well. Therefore, the clan was reborn although the initial blood line had been lost. The new clan survived until the planet was destroyed in year 12328.
The Klisis is covered very well in Cecil arc. Below stories deal directly with the clan.
[Cecil arc]  [Swordsmanship] 
[Cecil arc]  [To Venus] 
[Cecil arc]  [Mirren] 
[Cecil arc]  [Fall of the Klisis]