Have you had any communication with the HR department during this 3-month period? It should not be a significant issue if they simply forgot to process the relieving activities. They can process it and relieve you from the company quickly (2-3 days). Then you may consider extending your services for that short period.
In any case, it is essential that the employer responds to the resignation with either acceptance or rejection, providing a valid and clear reason. This letter generally also indicates the last working date. If you have received such communication from HR, then the notice period may be calculated starting "after the date of acceptance" and not "after the date of resignation."
If the employer fails to do this, and if they also do not respond to the letter format suggested by Gia in the above post, then you are free to stop work after the notice period as specified in the contract. If you choose to do this, please write a letter to HR stating that you did not receive any rejection response within the designated period. Therefore, the resignation is considered accepted, and as per the contract, you would like to discontinue your services after the notice period. You can still obtain a relieving letter and F&F settlement later.
Regards,
Amod.