Can HR remove from job without giving notice period which is offically mention in appointment letter

My appointment letter says "During probation, your services can be terminated at a months notice on either side or equivalent pay in lieu thereof and after confirmation at three months notice". But now the organization says they don't have sufficient projects to entertain you & give resignation or else I shall b terminated. Also as rule I shall be given a three months notice period with full monthly salary but they asking me to either take one month salary, considering a month notice period or else three month notice period without salary for those three months. I require time to find another job as I am told to resign suddenly without giving prior intimation, hence I prefer 3 months legal notice period with full salary. HR is not considering the same & forcing to choose any of those two options. can legally I ask the management for 3months notice period.

You can legally ask management for anything you want but you may not get it. They're required to do what is in the labor contract you're working under. In the absence of such a contract, it would depend on the law where you live. If you're in a union take your question to them, otherwise the labor board where you live or a lawyer.