It's been a long time since I read the manga and now I'm wondering about their power's name. Is it because they're prisoners and they are considered sinners?
As stated on the wiki (under trivia)
The name of this power refers to its origin, as the Wretched Egg represents the original sin or roots and the branches that later came from them. It also refers to how insignificant amount of power one Branch possesses compared to that of the Wretched Egg's. source
What is the original sin it came from ?
The Wretched Egg refers to the original sin, which is the sin of Adam and Eve in Christianity, resulting in the fall of man. source