Company wanted me to release without serving notice period: without paying me notice period salary

I resigned from my company, official notice period is 2 month. As per there offer letter i got joining date after 2 month in new company. but now my current company wanted me to release early within a month. as per this i will not be paid for 1 month as my next job start after 2 month. Can you please help me on this? Below is there offer later terms : Notice of Termination a) An employee shall not leave or discontinue services without giving notice in writing of his intention to leave or discontinue the service. Period of such notice will be minimum One month for all employees except employees on contract basis, who would be required to give 15 days' notice, who have rendered service for continuous period of 3 months or more. However, no offset of the unused leaves shall be allowed. b) In case of shorter notice competent authority shall have the right to accept such request on payment of such compensation not exceeding the Cash Component to the extent of shortfall in notice period. The competent authority shall have the right to waive such notice period. c) The period of such notice shall be two months for all employees except employees appointed for contract employees and trainees.