You have not signed appointment letter 

you are not required to serve 3 months notice period 

return the laptop received by you 

If you can prove by documentary or other evidence the job offered you is not the same for which  you were appointed you need to pay for any notice period. Default is on the part of  Y, on that ground you are excused from serving any notice period of paying for notice period.

If you mean to say “just 1 day” you worked for X, in that case you have accepted the employment. But there is  contradiction in your claim when you say that, “I have not worked on anything, no set up has been done on my system.” For proper advice clarification on above point is  necessary.

There is no letter signed by you that you will serve the 3 months notice period 

further company can accept salary in lieu of notice period 

refuse to serve the notice period 

let company file case against you 

Dear Client,

If there is no appointment letter or offer letter, then your services are deemed to be temporary in eyes of labor law. And they can not take any action against you or ask you to serve any notice period.

Thank You

- The job offer does not mean that the employment relationship between the employee and the employer has started unless there is a written proof which clarifies that the offer has already been effective and the burden of proof shall be borne by the party who is claiming starting the employment relationship.

- Further, It is only an offer, after signing; it becomes unconditional acceptance of an offer in accordance with the general rules of contracts,

- Hence, if an employee refrains from joining the work with the employer or if the employer evades letting the employee join the company, in this case, the party who breaches the obligation has to compensate the other party for damages caused or loss of profits.

- Since, you have got only a Job offer, hence until you accept the same after signing, the said Company cannot harm you in way, and the notice period is applied in your case 

- If you got any notice from the said employer , then reply the same that you have your legal right to join or leave the company before entering into a contract. 

You have been trapped by the employer who had  thrust a laptop to you to show that you are employed by him and that you are bound by the employment conditions.

However the legal fact is that you did not sign the offer letter (which was not given yet to you), therefore you are not in any manner be termed as an employee of that organisation nor you are bound to comply with the unjustified  conditions that the company is trying to impose against you.

Since you are not even an employee, you need not even tender a resignation letter nor have to even formally inform the comp[any about you leaving the same.

You may just handover the company's assets to some responsible person and walk out of the company.

Since there is no evidence to prove the employer-employee relationship they may not be able to take any legal action against you to recover the threatened money towards notice period, hence you may remain unworried about it.

You should not have bargained or negotiated to the HR, because all her talks are senseless.

If they have generated the employee ID then it is there problem for having generated the same without the employee not accepting the employment yet by signing the employment offer letter.

Therefore you do not even have to listen what she says.

Her statement is absurd in this regard.

If at all she wants to take any action on this, you ask her to proceed against which you can challenge the same as per law.

As opined earlier they do not have an y documentary evidence to prove the employer - employee relationship hence you do not voluntarily go for any negotiation and get trapped by making such commitments even orally.

If you do not want to go there, you cannot be forced by them so you better leave the company once for all 

You can refuse to give 3 months notice and buy the said notice period by paying basic salary

if the role in Y is different from what was originally offered to you, then this amounts to cheating 

the employment terms of Y are not binding on you

you can tell Y that they can take legal action against you as they deem fit and you will repel such legal action and in fact file a counter claim against Y for fraud and cheating 

this is a case of fraud. and when there is fraud, the contract is not binding on the employee

infact you should serve a strong legal notice to Y and mark that to the local police station 

You don't need to serve notice period if you did not signed offer letter or any employment agreement. You are bound to serve notice period only if you agreed to the condition. If there is any written communication between you and the company about joining and notice period then you will be bound to follow that. Otherwise you are free to resign.