State BJP General Secretary Surajnandan Mehta filed a case in the court of Patna Chief Judicial Magistrate Rama Kant Yadav alleging that her remarks would promote enmity between groups and lead to breach of peace.
Court sources said that the matter was expected to come up for hearing tomorrow.
The case was filed under sections 153(A) (promoting enmity between different groups), 153(B) (imputations, assertions prejudicial to national integration), 171 (G) (false statement in connection with an election), 500 (defamation) and 504 (intentional insult with intent to provoke breach of peace) of IPC.
BJP has alleged that Priyanka had insulted Modi as he belonged to a backward caste, a charge denied by Congress which said she was only referring to his 'low-level' politics.
Another case was filed against Priyanka in a Darbhanga court.
Head of state BJP Fishermen community cell Arjun Sahni filed the case in the court of Darbhanga Chief Judicial Magistrate Shailendra Pandey against Priyanka levelling similar charges.
This case also expected to come up for hearing tomorrow.
Priyanka Gandhi, the daughter of Congress chief Sonia Gandhi, Monday said Modi had insulted her "martyred" father Rajiv Gandhi, and that the Congress booth workers in Amethi would give a befitting reply to his "low-level politics".
"They have insulted my martyred father on the soil of Amethi. People of Amethi will never forgive them for this wrong act. My workers at booths will reply to this despicable politics. Each and every booth of Amethi will give a reply," Priyanka Gandhi had said.
Former prime minister Rajiv Gandhi had represented Amethi in parliament.
In his speech in Amethi Monday, Modi had attacked the Gandhis and accused the Congress of "arrogance".
He said Rajiv Gandhi, when he was a Congress office bearer, had "humiliated" the then Andhra Pradesh Chief Minister T. Anjaiah at an airport. Anjaiah was chief minister 1980-82.