The victims, aged 22 and 48, had been drinking at the Dahlak public house, in Stoney Rock Lane, Burmantofts, before the attack which happened in the car park outside between 12.15am and 12.33am in the early hours of January 1.
The suspect arrived at the pub earlier in the evening with a large group of men and had been ejected.
Shortly after midnight, the 22-year-old victim exited the pub and saw the suspect involved in a fight with another man.
The victim intervened and was stabbed in the back, head and hand.
His father went over to defend him and was stabbed five times in the back.
Both men needed hospital treatment for their wounds, which were serious but not life threatening.
The suspect was described as an Asian male, aged 19 to 25, 5ft 9ins to 6ft tall with short dark hair and a moustache and goatee beard.
He was wearing a white, waist-length, zip-up, padded jacket with fur around the hood.
Anyone who recognises the suspect from the CCTV images or who has any information that could assist the investigation is asked to contact Detective Constable 2942 Tyra Rahim of Leeds District CID via 101 quoting crime number 13180000228.