Lovers (Korean)- The main character is a high ranking gangster
Tree of Heaven (Korean)- The gangster storyline starts a few episodes into the drama
Two Weeks (Korean)- The main character is a low-level minion in the crime syndicate; starring Lee Jun-ki
Dr. Kkang (Korean)- The main character is a former gangster trying to change his life
My Boss My Hero (Japanese)- The main character is uneducated and, to take the position as the future leader of the yakuza, he returns to high school as an undercover student
I can't say I liked all of these dramas, but they are what you're looking for. If you pick one of these, I hope you enjoy it. Good luck.
