To force for resign company after joining 15 days

Hi Sir / Maim, Basically I am from Uttar Pradesh. After shortlisting resume, On 15 days back, A reputed company of Bangalore conducted the Interview process via telephonic and after clearing all rounds I was selected. Next Day, they released offer letter with Join company within 3 days and also complete all complete initial Joining process on company portal. I completed all process and send resume as company format with insurance that i will join company on time. I came from Home via Air and join company on time. After that they conducted a client interview and i replied same answer as given in interview but they provided feedback to another HR that he is not able to give any answer as per project requirement and May be some other person was giving answer in place of him during interview. Now HR is forcing me to start resign process and leave company with 3 months basic salary but HR is not providing any official mail for it only telephonic communication. Could you suggest me, I should start resign process or not because I am sure that company can say that No, I don't promise to pay anything? Another question, Can we file a case against company from Hometown?