Today suddenly our HR had mailed to all the employees that after 6 days all employees' post resignation notice period will be changed
- from 1 month (old) to 3 months (new) for under probation employees &
- from 2 months (old) to 3 months (new) for permanent employees.

Even logically this seems to be too stretched up for IT service company based in the India.

My question is how much legal is this?

I googled but answers were for Indian labor laws which are not applicable to the IT company according to my knowledge.

Changing terms implies the change of contract with employees or retaining the terms you signed upon earlier. Everything else is noise and most certainly illegal.
If contract says you are ought to do what person A says and it contradicts other parts or country laws, such paper loses legal binding.
#notlegaladvice Not a lawyer here. Contact one.

i see it as the same as @vintprox.
from my knowledge there are two types of legal contracts: one sided and two sided.
one sided contracts are for example resignations, they are binding after delivery. Two sided are contracts like your work contract. They are binding after both parties have shown their will in word or paper. when they want to change the terms you need to agree to it. This "implicit" change of your work contracts can be legal, but in court there is no proof for this. In my case when i was getting an pay rise, by company send me an contract for changing the contract, just to have it on paper.

It is legal, but only after you sign the updated contract with the updated notice period.
Just make sure they don't add other things into the updated contract...

Fortunately (ish…) I live in the US, and there is zero legal requirement here to give any notice at all. Two weeks is customary, but only if you actually want to.

Like if you’re the only one who keeps the company afloat, you’re totally taken for granted, and just want to watch your asshole boss squirm and stress for two weeks 😇

Or, you know, if you like them. That happens sometimes, or so I’m told.

IT companies in India have some kind of exemptions from Labour Laws. So, they are free to choose their approaches to employment.

But as others said, all of it is binding only if you sign the contract document. You could refuse to sign. You would be asked to resign and the earlier contract you signed would be applicable.