Before you claim the international student benefit, confirm you can carry your student ID card, student visa and university acceptance letter at check-in, because the extra baggage allowance depends on all three.
Cleartrip sets lower fares on domestic flights for students, senior citizens and armed forces travellers. You have to select that category yourself, because it is not applied on its own, so it is easy to miss if you go straight from the search results to payment. Students must be above 12 and must carry a valid ID, seniors must be above 60, and the armed forces fare is for serving and retired Indian armed forces personnel and their dependents.
These special fares and the ordinary coupon discounts are two separate routes to a lower price. Some of the store's category offers carry a condition that they cannot be combined with any other offer, so you have to choose one route. Run the same search twice, once with the special fare selected and once on the normal fare with your best code applied, and compare the final total on the payment screen before you pay.
On international flights the student benefit works differently. It is applied as a code at the payment step rather than chosen along with the fare, so the two are not interchangeable.