NEW DELHI— McDonald’s Corp. has a baffling problem in India. It can’t get restaurants there to stop selling its food.

In August, after a lengthy dispute, the fast-food giant ordered its partner of 22 years in northern and eastern India to stop using the McDonald’s brand and system. But Connaught Plaza Restaurants Pvt. Ltd., which operated 40% of McDonald’s Indian outlets, about 150 restaurants, went rogue.

It has continued to sell Maharaja Macs, McAloo Tikki and McSpicy Paneer burgers under the golden arches—using the McDonald’s name and recipes.

“I cannot allow a large organization, this [multinational] monster, whatever you want to call it, to truly belittle our contributions,” says Connaught Plaza’s defiant managing director, Vikram Bakshi.

McDonald’s has accused Connaught Plaza, a joint venture between Mr. Bakshi and McDonald’s India Pvt. Ltd., of breaking agreements on financial management, internal controls and paying royalties, among other things.