Can a company serve legal notice for not joining even after accepting the offer letter with a penalty clause

What is the fact and context of this case?

Upon acceptance of this offer, should you fail or refuse to commence the performance of duties under this Offer Letter, you shall pay to the company two month's gross salary (INR *****/-) as liquidated damages, which is agreed and understood to be a fair pre-estimate of the damages suffered by the company on account of such action. Notwithstanding the above, the company retains the right to a file a claim for damages or take appropriate action in relation to any breach of the obligations by you under this Agreement.

Note: The above clause is on offer letter.

Did the Company impart any training on being selected in the company at the end of which you need to join as per Offer letter in consent of which you signed the contract or gave your consent to the offer letter?

Yes, I did sign on offer letter as an acknowledgement.

There was no training given by company.

But still, they might have incurred a certain expenditure in the recruitment process and once an offer is accepted, they might have planned a project in anticipation of your reporting as per acceptance.  Anyone can issue notice, and it is proper to reply to such notice through a local competent advocate.

If you've been in your job for less than a month, you don't have to give notice unless the contract or terms and conditions require you to. If you've been in your job for more than 1 month, you must give at least 1 week's notice. It's best to resign in writing, so there's no argument about when you did it.

See the point is that the company can serve legal notice based on a clause that has been dishonoured. But as per the clause that you have shared, in case the recipient has ample scope to contest it on merit. If any notice is served, better to reply it by an Advocate. However please, in case the employee wants  to resign, the termination clause should be referred and accordingly activity to be initiated.

There is nothing wrong in serving in serving a legal notice. You have the option to reply the same bringing your version on record.

There is offer and acceptance,and if you don't comply  with the offer the company is sure to issue notice, and it is uo to you to respond ornot, giving liberty to the company to take further steps. You cannot accept an offer and makes the company to wait till eternity for  you to act.