Janamejaya (Parikshit’s son and Arjuna’s grandson) has the same doubt after Vaishampayana recounts the story of the Mahabharatha at Sarpa satra. He asks the rishi to tell him in detail about the clan of the Vrishnis. Vaishampayana starts recounting to him the Harivamsha, which literally means the Vamsha of Hari.
The Harivamsha was also written by VedaVyasa and is called the Khila bhaag to the Mahabharatha, meaning supplement to the epic. Although it was written AFTER the Mahabharatha, it has the story of Krishna before the events of the great epic for most part. It has three parts- Harivamsha parva, Vishnu Parva and Bhavishya parva.
The Harivamsha is the text to read if you want a more detailed look at Krishna’s clan, his life events, his children and also the events in Balarama’s life. There is also a quick recounting of other avataars of Vishnu. The Harivamsha is also called the Harivamsha purana although it is not included in the list of the Puranas generally.