Need help against pvt company

Any how you have sent resignation letter as per shops and Establishment Act you see it may be 15 days notice. 

Another thread with similar query is at:

https://www.lawyersclubindia.com/forum/Serving-notice-in-one-month-old-company-87882.asp#.UitKWtKAqWM

Have you mentioned the reason that long hours of work which is against the law as reason in your resignation. Since the management as violated law in your employment you can approach the concerned labor officer and also make a written representation to your jurisdictional labor commissioner.

Actually I went there with the intention to verify the work culture physically. And before going to their office,while replying to their E-Mail having the offer letter (replied via E-mail that I have accepted the condition laid down in it) I did not mentioned the date of joining as I was not so convinced. So after going there for 3 days I found that they have long working hours(11 - 12 hrs) which was never mentioned to me. While in these 3 days I have not signed any register or bond, neither the company asked me to do so. But now they are saying that I have done by accepting the offer letters by in mail.

So on 4th day I being professional replied to them that "I don't want to be a part of your company because of my problem" so as to keep good term as per industry norms. But now the company is saying that I have to pay as per bond. But I have not signed any bond. And even not send them the offer letter signed by me (which is mentioned in the last clause).

Now they are telling me to come to their office give formal resignation and the two months salary. But when I have not joined in their company then why should I give so and even in this 3 days I have not taken any benefit from them even not taken my Post paid mobile connection.

I replied them the above line. 

But they are telling that in their log book they have register  me as joined from so and so date and also they have witness (their other employee) who will say that I have joined in their company.

Am I done anything wrong ?