Is It Fair to Pay a Penalty for Not Joining After Signing an Offer Letter? Seeking Advice

I had a face-to-face interview with a company, and they asked me to sign the offer letter. I requested some time to think about it, but they insisted that I would not receive the offer if I didn't sign it. Feeling confused, I signed the offer letter, which included a clause stating that if I don't join, I will have to pay a penalty of three months' salary.

Before the joining date, I informed them that I would not be joining, and now they are asking for the penalty amount.

Is the claim justified? Has there been any judgment where employees had to pay the amount?

Just ignore the demand. Let them file a case. On what grounds can they file it? When you have not even joined the company, how can they establish an employee-employer relationship? Just signing an offer letter will not create a master-servant relationship. Therefore, just ignore such emails.