Query regarding resigning immediately after joining and joining a new company

I have joined a "A" company and resigned after 10 days of working. I dropped a mail to HR and reporting manager stating last working day. There was no clause of notice period in the offer letter and i did not accepted any contract/appointment letter from them. I did not receive any asset or any monitory benefit from the company. Next day i joined a "B" company but the previous company tracked my joining and informed HR that I am absconding from "A" company. So HR called me and asked the details to which i provided them all the details. I also called HR and reporting manager of A company why they are doing it. They said they want one month notice from me or want me to apologize and join back. I said i dont want to join back.
Now after few days A company issued an absconding letter and sent it to Head HR of my company. Now my job is in trouble and current company may cancel my joining.
What are my rights that i can use now as previous company's reporting manager has made it a ego issue and is behind all this.

Dear friend,

Whatever is happening with you is unfortunate. Nevertheless, you are facing a backlash from your previous company.

Whenever a vacancy arises, companies spend their time and energy recruiting an employee. Your company "A" also did the same. However, your exit has made your efforts go in vain. Now they are retaliating from their side. If you had taken your manager into confidence on your separation, this retaliation would not have happened. However, through your sudden exit, you had served them a cocktail of surprise and shock. Now they are trying to get even with you.

The company "A", did not issue an appointment letter. Therefore, there was no requirement to serve the notice period. However, this argument is just technically correct. Probably, you had relied heavily on this technicality, and you were at the receiving end of that company.

The solution is on two counts. One is to go back to the previous company and beg a pardon. At the same time, try to take the HR of the current company into confidence and try to gain trust that you will not ditch this company too. Though this is a difficult task, you have no option.

Thanks,

Dinesh Divekar