Can i serve the entire notice period as per appointment letter?

I don't know about India, but in Australia and the UK you would be paid in the normal manner until the end of your employment - not as a lump sum at the end. Also, they cannot force you to terminate earlier than you have stated. If they do so, they will have to pay you for the full three months (so long as you did not terminate your employment earlier voluntarily). Also, again in Australia and the UK, they will have to pay you for any unused leave allowance. It sounds to me like they are trying to save themselves some money - don't do it unless you really want to.