Absconding mail.

Hi sir, I joined a recruitment consultancy in march 2018 in Delhi. I worked there for almost 1 year till Feb 2019. In Feb I took leave for a week to go to my cousins marriage but as my father was not well we were asked by the doctors to take him to vellore. As he is a govt employee referral procedure we're taking time so in mean time we visited Delhi for 1day with him to consult his endocrinology doctor who use to see him in Delhi. On that day I visited my office to update them the status f2f to them. Next day we left for vellore. His condition was so serious that doctors were kit able to understand what happened to him it took almost 15-20 days and I was not sure how much time it is going to take so I decided to resign as i need to be with my parents. I dropped them mail and mgs on WhatsApp. I didn't received any mail from them till 15 days. By that time my father's condition started becoming better. And doctor told in every 3 months he need to be here for checkup. So I decided to join a job in bangalore so that I can take care of them whenever required as coming from Delhi to vellore in every 3 months will cause mu h expenses. I called them and updated them that I joined a company in bangalore. But I got a mail from them of absconding and they asked me to come and serve complete 2 months. I requested them mant times but they use to send mail in the very 15 days blaming me that due to me they faces loss and I am working as dual employment which is illegal. I was afraid so I said I'll pay you 2 months of notice period but I don't want to pay as they already told my current company that they are going to file a case on me as i absconded. But my current company don't have any issue as I already told them before joining every thing. But they are sending amil in every 15 days for money 2 months of salary which is 34000 rs. Please help me i dont need any F&F or any relieving letter from them what can they do. And what should I do.