Hello cs_jai,
There could be quite a few reasons for companies to relieve someone early [before the Notice period], like:
1] Want to push the employee out ASAP--could be a security risk [like Simhan mentioned].
2] performance-related [what would this guy do staying here now, except taking salary?]
3] the resignation could be in-tune with the HR's lay-off plans--saves them the trouble of laying off the employee [more prevalent in IT sector].
AND maybe a few more.
Coming to your queries:
1). Whatever they are doing is correct or not?
I don't think this is a right/wrong issue. Legally the company would be covered [check your Appointment Letter--usually something like '.....at the discretion of the company/management......' would be mentioned].
2). Am I eligible for money of remaining days I am not serving.
Like Simhan mentioned, pl check your Appointment Letter.
But why do you want the salary for a period you haven't worked here? Suggest look @ this aspect/point in another way.
You would have got another job which is the cause for this resignation, in the first place. And i presume I can pretty comfortably assume that the new Offer has a better CTC than what you are getting now. So maybe this could be your chance to get into the new job & start to draw a higher salary ASAP, than waiting until 3 months--just give this a thought.
But in case you want this company to pay you the 3 months salary AND yet join the new company earlier & get the advantage what I mentioned above, all I can say is: stop getting greedy......that's the surest way to anyone's downfall in the long-run.
All the Best.
Rgds,
TS