Am I liable to pay notice recovery amount after leaving the company in 2 days of onboarding

My question have multiple parts: 1. I was working in a organization A and I received an offer from Organization B. Though I didn't like that too much but I thought that either HR of Organization B re-tructure of CTC or I'll find another organization with improved structure of CTC and not more than 2 months of separation notice period. With these thoughts, I got another offer at the day of joining of Organization B. 2. I received the offer letter-'Letter of Intent' for joining the organization B with the expected date of joining 20th July'22. However I communicated that I mayn't be able to join before 22nd Aug'22. Even after that, No new offer letter or joining letter issued with the latest date of joining. 3. Also I was not in favour of serving any kind of notice period more than 2 months post on-roll with any of the organization and I asked the same to HR but there were no response from HR side. HR was completely silent on that. 4. With the assumption that it is a big esteeed organization and it may not have the notice period more than 2 months, I joined the organization B on 23rd Aug and I received another offer on the same day. I evaluated the offer and confirmed to Organization B on 24th Aug that I am moving ahead with organization C and I am dropping the joining with Organization B. And till that time 24th Aug, Neither I received the new offer letter with new date of joining nor I received or signed the appointment letter. And I informed the HR, line manager for the same and I submitted my laptop and all the assets back to organization B (which was sent to me by Organization B right after releasing the offer to me) on 25th Aug'22. 5. I didn't participate in any of the operational things of Org B and its just 2 days where I havn't signed the appointment letter and didn't complete any of the onboarding activities as I already received another offer on the same day. (Though there were background verification, where I submitted the HR forms at the time of offer release i.e. during 27-28 Jun'22). After 20 days, I receive a 'Full-and-Final' statement letter from Org B over the email stating that I am supposed to Pay 1L Rs back to organization B. 6. Though I completely understand that hiring a right candidate and waiting for that candidate is a crucial and time consuming process, but my question as mentioned below has its legal questions: a. Am I liable to pay that 1L Rs to Org B, considering the fact that I didn't receive & sign the revised offer letter and nor I signed any Appointment Letter. And There was no clause of separation mentioned in the Offer letter and neither responded by HR while asking. b. In case, If I doesn't pay the amount to Org B, what could be the consequences. Will it impact the future job prospects or my credit score. c. Is there any possibility that Org B can sue me in the court.