Yes I know Hyuuga are a canon clan but here I am targeting a non-canon branch of the clan. I've moved the background to the end rather than between jutsu and location as it is the longest section. (Note: I am not ready to say that this is as finished as I want it to be so please do not comment about it yet.)
Clan Name: Hyuuga (The 3rd branch. Sometimes refered to as the satanic branch out of hate from the other branches. But somehow 3rd branch has become the most common name, uncreative as it is.)
Members: Rioichi Hyuuga
Location: Leaf village
Jutsus: The Gentle Fist and Palm tachniques
Skills: Byakugan. (If I have to explain the Byakugan to you, you have a LOT to catch up on.)
Background:
A branch of Hyuuga with a family line that dates back as far as any other branch. This branch was once framed for an assassination attempt of the Feudel lord of fire by an ancient enemy clan known as the Kouseki clan. Because of this the country had requested to the Hokage that the Hyuuga be executed. At the time the Hokage was in fact among the 3rd branch but persuaded the feudel lord to have only the 3rd branch executed as they were working independently and in fact stated that he would allow himself to be removed of his position but this noble act allowed he alone to remain within the village.
That man was Sonkei Hyuuga a legend among the 3rd branch for faking the entire execution of the branch to allow it to escape the country and travel around the world until they were forgotten. To ensure they were forgotten he destroyed all records of both the execution of the branch and the assassination of the feudel lord. He then faked his own death with genjutsu the same way he faked the execution and left the Leaf Village to meet again with his branch for the last time. The choice to leave his wife and new born child was tough but he needed to make sure that any ANBU who may have discovered the truth about the execution and came after them would follow him and not the entire branch. Luckily this did not happen but Sonkei could no longer find his branch as he no longer knew where they had gone. So he traveled the world alone kept alive by the peaceful feeling from knowing he had saved his family.
The branch itself went everywhere for many decades. This brought many difficulties to the branch and much suffering. They covered up their pain with anything they could. They tried starting their own occult rituals. They studied some dark beliefs and practices. But they found one thing that gave them a sense of importance, the tailed demons. For as long as they travelled they practice anti-bijuu techniques, seals, and passed everything down through the generations. They hunted the bijuu and sealed away as many as they could into a statue that would do no more than contain the demons and keep them seperated from each other or implant them into others whilr also being able to take demons out of jinchuuriki without killing them. The statue was left to them by Sonkei and was all they had left of him. With it they captured as many bijuu as possible but this was, unfortunately, less than five bijuu. they had hoped to get them all and seal the statue with the depths of the world where it would not be found but they could not and they wouuldn't withot all nine. Eventually this had to be given up on as they could not continue to hunt bijuu without risking the survival of the branch. The anti-bijuu techniques were kept in scrolls but never again learned or used. These scrolls were passed down and never lost to time.
They travelled across the continent and even to other continents. Until after two centuries they were found by the Hyuuga still within the Leaf Village and brought back and hidden until one day one child of the 3rd branch revealed their existence to the Village. They were safe now and could live like their ancestors had.
This child's grandson is now the branch leader and in fact a direct descendant of Sonkei Hyuuga who was now simply a family legend. The child saw the records the branch itself kept and learned of Kouseki as all other branch members did. This is why when he discovered the feudel lord was in fact a member of the Kouseki clan he attempted to assassinate him alone and to allow the blame to fall on he alone. But he still got the entire Leaf Village involved afterwards. War broke out and soon he came face to face with the legendary Sonkei himself. The man's chakra had granted him life extended beyond anything one could believe as he still appeared as young as when he was Hokage.
Together the two, along with the Hokage, fought and killed the Kouseki leader. When everything the Kouseki caused was undone Sonkei left to kill the remainder of the clan. The only damage that could not be repaired for the Hyuuga clan was the death of the clan leader, Yokoku, in battle. This death was covered and hidden from anyone outside the clan except for the Hokage. Yokoku had no children born or unborn and so the clan could not pass down the position of leader traditionally and is now deciding who among the branch leaders will become leader of the clan. This would make that leader's branch the new main branch and would affect the entire clan. They are choosing between the main branch, the cadet branch, and the 3rd branch leaders. But fighting and disagreements have broken out over this and if left with no solution will escalate to the point where the Village itself may have to take action to control the Hyuuga. Hopefully they can agree soon.