Notice for not Serving Notice period - what should I do as I have already joined somewhere else?

I had recently joined a startup of around 10 people based out in Gurgaon. My notice period in that organization was 3 months. I resigned from the organization within 2 months without serving any notice due to bad behavior of manager.
When I mailed them the resignation letter, the HR mailed me back asking to submit access card and drawer key only. There was nothing mentioned about serving the notice period in HRs response email.
After one month of resigning from that organization, they are sending me a notice via courier asking me to serve the notice period of 3 months or pay them compensation in lieu which is amounting Rs. 2 Lakhs. Could you please tell me what should I do as I have already joined somewhere else.
Is this even justified to send such a notice after 1 month of resignation? Please help me.

Further, please note that the notice period of company was as below:
"For employee, it was notice period of 3 months while from employee's side, it was 1 month". Is such a notice period even justifiable?
Thanks

Such notices from employer have no legal validity.
Ignore for the time being.
In case any further notice or issue comes up frame a reply in consultation with a labour advocate.
In my mind the compensation asked is simply a figure out of their mind and has no bearing.

Since, you left the Company within two months of your joining, you need not serve three months notice. And more over they took your access card and drawer key, it amounts to taking over your responsibilities.
Probably, you need to serve one month's notice or salary in lieu of your resignation.
However, if you can provide a copy of your appointment letter, it would be easy to understand and suggest you properly.
Further, you may ignore two months service with them.

Dear Nathrao and Dayanand Sir,
Thanks for your response.
They have sent me 2 letters one via speed post and another via courier with same date. I don't have any company assets' etc. in possession, I don't know why are they mentally harassing me. Please tell me if I need to respond to this or what should I do.
I don't need any experience, relieving or settlement from them. I am not even showing that experience in my CV. Attached is the appointment letter for your reference. Please suggest me. I need help.
Thank you

Dear Friend,
I have gone through the appointment letter, wherein it is mentioned as 30 days notice from Employer's side and 90 days from employee's side, which is legally incorrect and unfair labour practice.
Please ignore them, if you still need any assistance legally, pleases do write to me on mail ID [Login to view]

Sir,
1. In my company, one employee submitted resignation with notice period of 30days. But the company relieved the employee before completion of NOTICE PERIOD. Is it considered as Retrenchment or Termination? Is he approach labour court for 25F benefit?
2. The management given verbal notice of 3mnths to one of the 33years worked (present designation is Assistant Manager - Accounts). is he approach fr 25F benefit?
Chennai