Deadman Wonderland Akai Knife Tsukai

While we will probably never see a second season of this great anime series, there was an OVA released as well from it.

Called Akai Knife Tsukai, it follows Senji in his days before being incarcerated in deadman Wonderland, when he works as a police officer.

Two years after the catastrophic tidal wave that swept over Japan, police officer Kiyomasa Senji is trying to make the world a safer place. Using his Branch of Sin powers, he stops criminals in whatever ways he can. After rescuing a boy named Izuru Tsukiyoshi from a gang called Goreless Peace, the conflict between Kiyomasa and his adversaries heats up rapidly, to the point of being explosive.







Offering a glimpse into the past of the future Deadman, the story follows Senji, helping to further develop the reasoning that drives his actions later in life.

A one episode of 20+ minutes story, this does give some insight, though it doesn't tell exactly how he got incarcerated.  Though it does give a hint at how his clock got ticking...