Resignation- Notice Period

Hi. I am working in an old private sector bank as Officer Scale 1 since 2010. I got an opportunity as Officer Scale 3 in nationalised bank. I put resignation notice last month and requested my HR to relieve me immediately and i am ready to pay 3 months salary. They did not consider my request and quoted the agreement signed by me which says "In all the cases the management reserves its right to terminate your services at any time during the period of probation without assigning any reason there for, by giving one months notice or one month's salary in lieu of notice. Services of an Officer can be Terminated by the Bank at anytime by giving THREE months notice or THREE months salary in lieu of notice after confirmation. If you wish to leave the services by way of resignation or otherwise, you have to give three months notice in writing and serve the entire notice period". They replied me that I will be relieved in April and I should take only 1 leave per month and if I take leave other than that my relieve date will be further extended. My new employer is forcing me to join immediately and informed me orally that he cannot give time extension. I have forwarded my request letter along with letter received from old bank and requested my new employer to give me time. He orally told me that he will give me 10 to 15 days time. I am in a dilemma. Kindly advice me.