JERSEY CITY — With Prime Minister Narendra Modi of India set to meet President Trump on Monday for the first time, many Indians in communities like this one have had high hopes for the relationship between the two leaders — both of whom swept to power as media-savvy political outsiders pledging to revive their national economies.

In a string of storefronts here in “Little India” that pay tribute to Hindu deities, Yogi Patel, 52, runs the Laxmi Pan Center, which is named after the goddess of wealth and sells a betel nut breath freshener. He has lived in the United States for 32 years and is a strong supporter of Mr. Trump.

“Trump is doing the right thing. He’s doing good for U.S. citizens and America,” he said, switching between English and Hindi to explain that he grew up in Gujarat, the state that Mr. Modi led as chief minister before the 2014 election. “And I am from both countries.”

But as Mr. Trump has tried to crack down on immigration and withdrawn from the Paris climate agreement, singling India out as a country that has gained unfairly from the accord, the meeting of the two leaders with nationalist leanings and sizable social media followings has taken on a more complicated tone for others in the Indian diaspora.