Matou Byakuya

The true father of our beautiful wakame, Matou Shinji.
Though his suitability as a magus was inferior to his younger brother Kariya’s, he was forced into becoming the next family head after Kariya turned his back on his inheritance and ran away.
However, this wasn’t a terrible deal for Byakuya. Since Zouken never expected anything from him to begin with, he was never actually taught anything. He was essentially a glorified assistant, while the real responsibility of being the successor was passed on to his adopted child, Sakura.
Probably, Byakuya thought that the shame of being a family head in name only—as well as his abhorrence of sorcery—would be more than compensated for by his
access to the Matou fortune and a life free of worries. But ultimately, it seems it was far more stressful than he ever could have anticipated, and he ended up taking refuge in alcoholism.
He made his first and last appearance in the fourth volume. At first, the scene was going to end with Kiritsugu going to the Matou mansion while searching for Irisviel, but turning up nothing. However, on a whim I decided that I hadn’t written enough violence that day, so Byakuya, a character that never should have appeared at all, was thrust onto the stage as a sacrifice. My deepest condolences, Byakuya.

Fate/Zero material: Fate/Zero Encylopedia

Current head of the Matou Family and Kariya’s brother. He tortuously trains Sakura in the bug cellar to prepare her as the successor of the family. When Kiritsugu is searching for Irisviel, Byakuya is tortured by Kiritsugu and loses his right hand.

Fate/Zero Animation Guide II: Glossary of the holy grail war II