VARANASI, India — It was 4 a.m. at the Yadav family home down a narrow lane in Varanasi, the constituency of the Indian prime minister, Narendra Modi. Vijay Yadav, 30, cut buns and toasted them one by one on a gas stove with the help of his mother, Kamla Devi.

Mr. Yadav is a staunch supporter of Mr. Modi, and the snacks were for about 100 party observers at counting stations on Thursday for what would turn out to be a landslide victory for Mr. Modi and his Bharatiya Janata Party — both strong proponents of Hindu nationalism in a country that is roughly 15 percent Muslim.

The Yadav family’s roadside tea stall — which his father, a recent Modi convert, has been running for decades — is decorated with several fading pictures of Mr. Modi, including a couple on the refrigerator beneath icons of several Hindu deities. The store sign also bears the prime minister’s nickname: NaMo Tea Stall.

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