The one-sided extension of the Notice period is not supported by the law and is therefore void. As you stated that you delivered the notice as required and that the notice time had ended, it is important to highlight that you should have documentation proving that you served the notice and the date on which you did so. For instance, sending them a letter alerting them of the same is sufficient.
However, if you have personally sent it and you don't have a letter of response or any other documentary proof, strive to obtain one. You are under no obligation to continue working for your current employer once this is over. They are relieving, so it makes no difference if you are not. Simply send them a letter stating that you gave me notice in a timely manner and that despite my request, you have not released me.
The Hon'ble Supreme Court of India decided whether accepting a resignation is required in cases where an employee has issued a notice of resignation in its decision dated November 01,2018, in the case of SanjayJain vs.National Aviation Co.of India Ltd[3].
The Apex Courtex plained its stance on accepting resignations, stating that "to resign is a right of an employee who cannot be forced to serve in the even the is not willing until and unless there is some stipulation in the Rules or in the terms of appointment or disciplinary proceedings are pending or contemplated which is sought to be avoided by resigning from the services"
To conclude, the condition of working 60 days during the contract will be binding between the employer and you, so stick with it.