I agree with the suggestions given by the members above. This case evidently shows how poor the employer's practices, work style, and processes are. Without proper background verification (if they have a "Background Verification System"), they should not have offered the appointment letter or hired any candidate.
If the employer found anything wrong with the provided educational details/documents by the candidate, or anything that failed authentication, they have the right to take action against the employee. They should supply the details to the employee/candidate professionally to set an example for others.
They should have issued you a Termination Letter, but they failed to do so, and they are wrong at this point.
Secondly, if you are not at fault (as Mr. Rangarajan mentioned, only you know your situation) and they have not issued a "Termination Letter" with necessary details and reasons, you must try to obtain it.
I suggest you write another letter to the HR Head/General Manager with complete details, enclosing the email communication and any other correspondence you have had. Request them to provide the details of what caused your termination. Also, mention the name of the personnel who attended your interview or finalized all the details. (Post it by registered AD)
Note: There is no need to write directly to the CEO or similar authority but to the HR Head/Manager only, as they are the right and concerned authority.
If they fail to reply to you, you must file an application to the local/regional Labour Commissioner/Inspector, sharing all the details and referring to the appointment letter offered to you by the employer, with a CC to your employer. You can also visit them personally with all the original educational documents and work details.
Lastly, do not lose hope and confidence but move ahead, as Mr. Sachin said above. This was not the only job you could have had, and you can find many good jobs. However, I would say that taking action against the employer or solving your problem, as suggested above, can be secondary because getting a good job is most important for you now, in my belief.