Join For 3 Hrs. Leave Co. Co Asking For Amount

I joined co and after 3 hrs due to ill health left and did not go to office for next 6 days. Sent mail to company about my unavailability with a request to discontinue from job. Did not signed any offer letter. After 4 month company sent a letter asking me to pay an amount. What is the justification.

Since you have emailed and stated your inability to continue service, it proves your employment with the company even though you have not signed any offer letter.
It will deemed that you are/ were an employee and bound by the terms (notice period) of appointment even though in actual terms you have not received any.
I presume that company is asking you the notice pay since you have not served the notice period.
Without seeing the email you sent and the letter of the company (and other documents if any), it is difficult to advice. But if you do not give a proper reply from legal point of view, you might be in trouble in future.

Unless the company signs any "employment contract" or gives "offer letter", how can you establish it was "employee / employer" relation? and thus no labor law applies.
It could very well be a contractor or freelance arrangements?
In my previous company too, the company never gave any offer letter / agreement / payslips. Seem it's normal practice amongst employers in India

It is a usual practice in India that millions of people work here without any valid documents (like appointment, id, esi, pf etc) from the employer, but as the Apex Court, that does not mean that there does not exist any employer employee relationship between them. If there is no direct evidence of relationship, then comes the circumstantial evidences.
In case of BSNB herein above, it is the company who has sent him letter to serve the notice period or pay the amount hence the question of employer employee is established and moreover when BSNB has himself sent an email to the company expressing his inability to continue service.
Moreover, many companies do not give any offer letter/ appointment/ payslips etc. as an usual practice in India, but this usual practice does not make it neither ethical nor legal.

The company must have mentioned a valid reason in their letter for demanding money. Please go through it carefully and inform the forum so as to give you appropriate view