According to the Bhagavata Purana, within a span of 10 days of Pradyumna's birth, he was abducted by the demon Shambara. He was then cast into the sea and swallowed by a fish. Under the protection of Lord Krishna, the fish was caught and purchased by Shambara. Pradyumna was found inside the fish and was raised by Mayavati, Sambara's cook and the incarnation of Rati, Kamadeva's wife. When Pradyumna grew up in a short while, Mayavati told him the truth about their identities. He battled the demon Sambara and killed him by severing Sambara's head with his sword.
Pradyumna's first wife was Mayavati, the incarnation of Kama's wife Rati. At first Pradyumna objected, but he was convinced when she told that she destined to marry him. He also married the Rukmavati, the daughter of his maternal uncle, Rukmi. It is said that Rukmavati found his valor, handsomeness and charm beyond words and insisted on marrying him at her swayamvara. With her, he fathered, Krishna's grandson and favourite, also considered a vyuha avatar of Vishnu, Aniruddha. Prabhavati was an asura princess, she fell in love with Pradyumna and he eloped with her.
Soon after Pradyumna became a constant companion of his father Krishna and was well liked by the people of Dvaraka. Pradyumna was a mighty Maharathi warrior. He possessed the extremely rare Vaishnavastra which is the most powerful weapon in the universe. Also he was one of the very few people to know the secret of the Chakravyuha. According to Mahabharata, Pradyumna trained Abhimanyu and Upapandavas in warfare, when the Pandavas were in exile. But Pradyumna did not participate in the Kurukshetra War as he went on a pilgrimage with his uncle Balarama and other Yadavas. But he was an active participant In Ashwamedha Yagna which was later conducted by Yudishthira.
Pradyumna defended Dwarka against Shalva, the king of Salwa Kingdom, along with his father, uncle and brothers. In the Harivamsa, Pradyumna alone repelled the attack of Jarasandha.
Pradyumna was later killed in an intoxicated brawl, along with all the other members of the Yadava dynasty. His grandson Vajra was the only survivor of the Yadu dynasty after this incident.
One of the epithets of Pradyuma in literature, such as in Harivamsa 99, is "Makaradhvaja", meaning "he whose banner or standard is the crocodile". A pillar capital with the effigy of a Makara crocodile found at Besnagar near the Heliodorus pillar dedicated to Vasudeva, is also attributed to Pradyumna. In Mahabarata too, the Makara is associated with Krishna's son and Kamadeva, the God of Love, suggesting they are identical.
As per the Bhagavata Purana, Canto 10, Chapter 61, Aniruddha was the son of Pradyumna and Rukmavati. He was later abducted by Usha (daughter of Bana Daitya and granddaughter of Mahabali), who wished to marry him. Usha's father, Banasura, however imprisoned Aniruddha, creating a battle between Lord Krishna and Lord Shiva. In the battle, Pradyumna defeated Shiva's son Kartikeya, who fled on his peacock. At the end of the war, Banasura lost and Aniruddha and Usha were married. (See Canto 10, Chapter 62-63 of the Bhagavata Purana).
Aniruddha is said to have been very much like his grandfather Krishna, to the extent that some consider him to be a jana avatar, avatar of Vishnu. Aniruddha's son was Vajra. Vajra was known to be an invincible warrior and was the only survivor of the Yadu Dynasty after the Yadus' battle. According to some sources, Vajra then had 16 idols of Krishna and other gods carved from a rare, imperishable stone called Braja and built temples to house these idols in and around Mathura so as to feel the presence of Lord Krishna. It is said that Pradyumna and Arjuna were equivalent in their skills.
Pradyumna is mentioned in Bhagavata Purana (Canto 10, Chapters 55; Canto 11, Chapter 30).
Krishn and Rukmini in right, narad in left and pradyumn and mayawati in the middle (after killing shambarasur)