A little-known Indian IT firm offered its hacking services to help clients spy on more than 10,000 email accounts over a period of seven years.

New Delhi-based BellTroX InfoTech Services targeted government officials in Europe, gambling tycoons in the Bahamas, and well-known investors in the United States including private equity giant KKR and short-seller Muddy Waters, according to three former employees, outside researchers, and a trail of online evidence...