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Sudhir Ojha, a Muzaffarpur-based lawyer, filed the prayer before the CJM court on Friday, which will hear the matter on January 3.
"The song 'Besharam Rang' of the film 'Pathaan' is objectionable and it hurts the sentiments of the Hindu community," Ojha later told reporters.
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The film has courted controversy in some parts of the country after the song was released, with protests being held over the content in it.
Madhya Pradesh Home Minister Narottam Mishra had recently frowned upon the colour of the attire of Padukone and actor Shah Rukh Khan in the song, calling for its "rectification".
Effigies of the actors have also been set on fire at a few places, including in Indore.