(This is a GoT AU for one of my other OCs, the Paladin, I won't really change much with the characters mention in her bio page, but just note that in this AU, the more magical aspects will be heavily reduced, such as the magical conduit thing that her sword has, along with the magical aspects fo her armor)

House Cadyern History/Origin

The Cadyern's are a branch of the Lannister family, the rulers of the West. They came to surface about 500 years before Aegon and his sisters counqered Westeros and united it under one banner. 

Karman Lannister, Lord of House Lannister, which was at the time, the royal family and Kings of the Westerlands. Had a bastard brother who he loved dearly, a man named Cadeyrn Hill of The West, worked as the general of the Lannister armies, often at the front lines to repel any invaders and such, earning fame as one of the brightest military rulers and strategists of the time. 

For his services and loyalty, rewarded Cadeyrn by making him a vassal of the Lannisters, given him his own lands, and allowed him to creat his own house. 

Cadeyrn became known at The Founder after that among his family. And in honor of the first Lord of their House, they renamed it to House Cadeyrn after he passed away, to remember his achievements. 

When Aegon arrived in Westeros and started to counqer the Six Kingdoms, the Lannisters and the Gardeners, the royal family of the Reach, joined forces to fight back the Targaryen invaders. The Lord of House Cadeyrn of the timem, a man by the name of Mathias Cadyern, had urged Loren, the King of the Rock, to not in open combat, over the fact he was worried for the dragons. Loren of course didn't listen, as he and Gardener amassed a massive army, but it was futile as they were burned alive by dragon fire. 

The Aftermath

After the Lannisters and the Reach bent the knee to the Targaryens, The Cadyerns had taken Aegon's interest do to their well known experience in combat and warefare, had requested them to join on the battlefield. After some arguement, the Lannisters allowed Cadeyrn to join Targaryen in battle, where they showed themselves as a great instrument in taming the Riverlands, where they were truly recognized for their military might and cavarly. 

Locations

The Cadeyrn's were given a decent amount of lands in the northern parts of the Westerlands, more spesifcally near the borders and the sea, to continue their duty as the guardians of their home

The home of their House is Liontooth Stronghold, located in the northernparts of the Westerlands, a little east of the border into the Riverlands

The keep itself is located on a hill, giving it the higher ground and advantage during a siege, protected by two walls circling around the keep, and made of stone. Along with this, there are only two ways in, through a stone bridge over a large gap between the hill and the mainland, with a part of the bridge buillt to be raised during a siege. and the other is a small gate leading down to the beach below on the back side of the Stronghold.

the Inner Wall that surrounds and conects with the main keep, has four high walls, allowing them to see any sort of large armies and fleets from all sides do to the fact Liontooth Stronghold is barren of most forests, except a forest a few miles east of them towards the border, the ground only covered in a vast field of green grass.

 It is made to defend a siege rather then the luxurious taste of their Lannister relitives. 

They do have a decent sized town/city a little outside the Stronghold, called Little Tooth, which is connected to the beach and small port, which is how the Cadeyrns earn their income, through fishing, merchants going through and the like.

Along with that, they have a few outposts/forts scattered around the northern parts of the Westerlands, and two large forts on the Riverland border. 

Military

The Cadeyrns are a highly military oriented House, do too the fact they are tasked with protecting the northern borders of the Westerlands, they have a large army of 4000 infantry and 1300 cavalry. They are knights, and while they are a smaller number, their cavalry is their strongest unit of soldiers, and every one of them are heavily disiplined and trained in the art of combat. 

Banner

Do to their origin and connections to the Lannisters, they made their banner the opposite colors, a white/silver lion on a field of blue

Their Words "Power, Progress, Peace"

Sword

Through some luck and reward, the Cadeyrns managed to find a beautiful sword, made from Valyrain Steel, which they took on as their family sword, and named it Caled, in honor of Cadeyrn the Founder's first born son, whom found the sword

(Now as mentioned above, some things will be changed when rped with this AU, the most noteble would be the fact that obviously, do to laws and traditions, Alys wouldn't be a princess, and not a knight.) 

(Even so, she is still the first born child of House Cadeyrn, and still a warrior and leader of their army, but she isn't recognized as a knight do to the fact women can't be knighted in the first place (the only exeptions having been Brienne of Tarth obviously.) 

(The Cadeyrns will not be a royal family in this either obviously, but a Noble House with close connections to the Lannisters)