The student discount program at Lufthansa allows a student enrolled in a US institution and those aged between 12-25 to travel to more than 470 destinations internationally for discounted prices. You will have to use your .edu University email and also have a valid student ID.
Student Universe routinely has discounts for student travel to India. Some of their current offers include: NY- Mumbai $714, NY-Hyderabad $726 and NY - Bangalore $699. Check their website to check out their current deals.
Flat 8% off for students on international flights originating from India. Student ID is a must and tickets must be purchased a minimum of 15 days before departure.
Air India just launched 3 new direct flights from JFK to Mumbai. They offer the AI Maharaja Scholar's offer (until March 2019) which allows 1 additional bag (23kgs max) on flights AI101 and AI102.