I don't remember Story well but I think In starting a chinese ninja kills every member of a village and there was only small baby left in the village, After seeing the baby (Wrapped in a Basket on the lake shore, I think it was girl) he chooses not to kill him and goes away from the city and raises the child in other city and works in his friends laundry, but the people he was with comes to kill the child. and he defends the child and city both.
I think you search for
After a lifetime of training in martial arts and swordsmanship, Yang (Jang Dong Gun) has eliminated all but one of his clan's enemies - an infant whose smile instantly melts his heart. Unwilling to kill her and unable to protect her from his own deadly tribe, Yang takes the baby girl and flees, planning to seek refuge with an old friend living in Lode, a frontier town in the American West.