The helmet, called the "Patka Helmet" derives from the helmets designed for Sikh soldiers, and have evolved in the last ten years to be the helmet of choice during counter-insurgency and anti-terror operations in both Kashmir and in the Northeast.
First, some explanations... the Sikh "turban" (called the "dastaar" or "pagadi"), is made up of two different parts. The outer wrapped turban, and the inner shroud. The pagadi is the orange headgear shown here in the Sikh Light Infantry's dress uniform:
In the Sikh LI, the circular metal ring worn on the pagadi is called the Chakram and is not part of the pagadi, but is the Sikh LI's unique regimental weapon and is part of the dress uniform. The chakram is an ancient Indian bladed throwing disk that was used in battles as a mele throwing weapon and today in the Sikhs martial art, Gatka:
Worn underneath the pagadi is a cloth wrapped around the head kind called a "Patka." The patka can be worn by itself, or during PT, or combat when the helmet is not required or it is too hot to wear, it is covered in a cloth called, remarkably enough, the patka cloth, worn (perhaps identical to) the 'doo rag' that's become popular in America. It's best to think of the pagadi as you would a uniform cover that is removed except for 'dress' occasions.
Here are soldiers of Punjab Regiment with their pagadis removed, and with the pagadi cloth:
Now obviously, in this modern age of balistics, a Sikh turban cannot be worn in combat. So an ingenious solution was developed; a headgear made of a ballistic strip manufactured from high-density, die-pressed phantom steel and kevlar was made for Sikh soldiers that would go around the pagadi, as is shown in the following photos also of Punjab Regiment:
As was soon found out, the Patka helmet offered superior protection around the forehead and sides of the head from shrapnel and debris from IEDs and mines compared to the helmet. The standard bullet-proof helmets only provided protection against 9mm weapons, whereas patka helmets gave superior protection against AK-47 to the forehead and rest of the head area. It is also remarkably light and easy to customize that allowed for a lot of the customization of kit that can be seen in deployed units.
As such, the Patka helmet has been unofficially adopted as the headgear of choice for
all troops on COIN and anti-terror missions, across all regiments and police units.
The Patka cloth/doo rag has also been adapted, mainly as fashion

though it does also serve the same sort of purpose as bandanas in keeping the head cool and sweat out of the eyes. This can be seen in the following pics of regular troops of Rajput Regiment, who aren't Sikh but are seen donning both:
Another example: here are Ladakh Scouts soldiers (ethnic Tibetan regiment) engaged in COIN ops on the LOC with Pakistan-occupied-Kashmir. Their Patka was used with a customized uniform kit suited to Himalayan winter ops:
Soldiers of armored and mechanized regiments wear the patka cloth as standard issue under helmets, due to the heat of desert ops:
Rule of thumb is, if you see a photo of an Indian soldier wearing a standard or ballistic helmet he is engaged in conventional operations (like in Kargil War photos, or patrols on the India-Tibet and -China border where infiltration is not an issue.) If he is wearing a Patka, he's engaged in COIN or anti-terror ops.