The incident took place in the Purani Bazar locality as the man, identified as Yogi Paswan, followed his daughter Priti Kumari (22) and his son in-law Vinay Paswan (26) some distance from his home and shot the two, Deoria police station in-charge Sujit Kumar said.
The couple died on the spot, he said adding the bodies have been sent for post-mortem.
The accused was concerned with the well being of his daughter at his in-law's place as she was pregnant for the second time after suffering a miscarriage allegedly due to lack of proper care by her husband's family, Kumar said.
Vinay, however, overlooked his father-in-law's plea and had left for his native place with his wife, he added.