The RJD won Araria parliamentary and Jehanabad assembly seat, while Bharatiya Janata Party (BJP) seized Bhabua assembly seat.
Following the victory, former state cabinet minister and Leader of Opposition in Bihar Assembly, Tejashwi Yadav, took a dig at the BJP and said: "To those who say Lalu (Prasad Yadav) Ji's name would be erased, I can say that Lalu Ji is an ideology."
Yadav also questioned the state government over its negligence towards corruption cases involving Deputy Chief Minister Sushil Kumar Modi.
He said: "The deputy chief minister is mired in corruption, but no action or probe is being conducted. We suspect that Prime Minister Narendra Modi, BJP president Amit Shah, Enforcement Directorate (ED), and Central Bureau of Investigation (CBI) will speed up their probe against us after this win."
He also took to Twitter to "dedicate the win to the people of the state" and thanked them for supporting Lalu Prasad Yadav-led RJD.
RJD's Sarafaraz Alam, the son of party member Taslimuddin, won the by-election in Araria, which was necessitated after his father's death, and the party's Suday Yadav defeated Bihar Chief Minister Nitish Kumar-led Janata Dal-United's Abhiram Sharna in Jehanabad.(ANI)