A mob held protests at a polling booth in a village in Paliganj area of the Pataliputra constituency and vandalised an EVM after some youths were stopped from casting their vote, police said.
A clash between rival groups occurred at Vayapur in the same constituency.
In the Nalanda seat, a mob ransacked a polling booth and held an official hostage for an hour as they boycotted the polls.
Clashes were also reported from Sasaram, Karakat, Arrah and Jehanabad.
At some booths, voting was delayed to EVM glitches.
Chief Minister Nitish Kumar, Deputy Chief Minister Sushil Kumar Modi and former Chief Ministers Jitan Ram Manjhi and Rabri Devi cast their votes in Patna on Sunday.
Union Ministers Ravi Shankar Prasad, who is contesting from Patna Sahib, and Ram Kripal Yadav, who is in the fray from Pataliputra, Yadav's Rashtriya Janata Dal rival and party supremo Lalu Prasad's eldest daughter Misa Bharti and her brother and former minister Tej Pratap Yadav also cast their votes here.
However, it was the first time when Lalu Prasad was not present to vote along with his family members. In a Ranchi jail after his conviction in fodder scam cases, he is presently undergoing treatment in a government hospital there.
A total electorate of 1,52,52,608 voters were to decide the fate of 157 candidates in Patna Sahib, Pataliputra, Arrah, Buxar, Nalanda, Sasaram, Karakat and Jehanabad constituencies.
Among the other prominent candidates are Union Ministers Ashwini Choubey (Buxar) and R.K. Singh (Arrah), former Lok Sabha Meira Kumar (Congress, Sasaram), actor-turned-politician Shatrughan Sinha (Congress, Patna Sahib) and former Union Minister and Rashtriya Lok Samata Party chief Upendra Kushwaha (Karakat).
Of these seats, the BJP had won six, then ally RLSP one, and now ally JD-U one.