Mishra and his sons Trilochan and Biranchi were earlier picked up from the ashram located at Jhinti Sasan in the wee hours and taken to the Commissionerate of Police headquarters here for questioning, Commissioner of Police R P Sharma told reporters.
The FIR was lodged against them at Balianta police station on the outskirts of Bhubaneswar by a person yesterday.
The police action came shortly after angry locals went on the rampage leading to a clash between followers and opponents of Mishra at Jhinti last night. Allegation of land grabbing has also been levelled against him.
Several vehicles were damaged and set ablaze by the mob in reaction to media reports on alleged immoral activities in the ashram.
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The protesters stormed into the ashram and ransacked parts of the building and other structures, drawing retaliation from the inmates, the police said.
Sharma said a case was also registered against the three under section 25 of the Arms Act after recovery of two guns and three rounds of live 9 mm bullets from the Ashram premises.
Meanwhile, the police has formed three special teams to probe the allegations of the Baba's acquirement of about 550 decimals of government land illegally and construction of the ashram on it.