According to the Brahmanda Purana, Jaya and Vijaya were the sons of Kali, and Kali in turn was one of the sons of Varuna and his wife, Stuta. The brother of Kali was Vaidya.
Curse of the four Kumaras
According to a story from Bhagavata Purana, the Four Kumaras, Sanaka, Sanandana, Sanatana, and Sanatkumara who are the manasputras of Brahma, visited Vaikuntha, the abode of Vishnu, to see him. Due to the strength of their tapas, the four Kumaras appear to be mere children, though they are of great age. Jaya and Vijaya, the gatekeepers of the Vaikuntha interrupt the Kumaras at the gate, thinking them to be children. They also tell the Kumaras that Sri Vishnu is resting and that they cannot see him now. The enraged Kumaras replied Jaya and Vijaya that Vishnu is available for his devotees any time, and cursed both the keepers Jaya and Vijaya, that they would have to give up their divinity, be born as mortals on bhuloka, and live like normal human beings. Vishnu appeared before them, and the gatekeepers requested Vishnu to lift the curse of the Kumaras. Vishnu said that the curse of the Kumaras cannot be reversed. Instead, he gives Jaya and Vijaya two options. The first option is to take seven births on Earth as a devotee of Vishnu, while the second is to take three births as his enemy. After serving either of these sentences, they can re-attain their stature at Vaikuntha and be with him permanently. Jaya and Vijaya cannot bear the thought of staying away from Vishnu for seven lives. As a result, they choose to be born three times on earth even though it would have to be as enemies of Vishnu. In their first life during Satya Yuga, they were born as Hiranyakashipu and Hiranyaksha to Diti and sage Kashyapa, and were killed by Varaha and Narasimha. In their second life during Treta Yuga, they were born as Ravana and Kumbhakarna, and were killed by Rama. In their third life during Dvapara Yuga, they were born as Dantavakra and Shishupala, and were killed by Krishna. It has been noted by many that the strengths of Jaya and Vijaya gradually declined with each subsequent birth. Vishnu needed one avatar each to kill Hiranyaksha and Hiranyakashipu. Born as Rama, he was able to vanquish both Ravana and Kumbhakarna. In his Krishna avatar, the killing of Dantavakra Shishupala and KANSA is not the main focus but more to reduce the 'Bhoobhara".
