How to exterminate/identify these insects?
They are some kind midge flies (chironomids (Chironomidae))... obviously a biting kind of midge fly. A species specific identification would require a much better image, or preferably- a sample of the actual insects.

I see that you live in India... that makes identification more difficult because entomology is not a thoroughly studied science there.

Generally speaking, midge flies are controlled in the larval state (before they become adult flies). They are a lot like mosquitoes; they lay eggs in stagnant water (sewage, ponds, and drains are common). The larvae are commonly called redworms.



Eliminating the (stagnant water) source of the midge flies would be the most effective control, of course. Otherwise, a natural control method (recommended) would be Bacillus thuringiensis subspecies israelensis which can be found in many box-stores... look for "mosquito dunks".