You have posted that:
"company asked me to leave the job"
Did you record the call/meeting (audio/visual)?
This implies that you were asked to resign.
Demanding resignation can be termed offence. Forced resignation can be termed 'Deemed Termination".
HR is not your employer. He/she is just another employee in the company and probably also not competent to sign appointment letter, termination.
You are well within your rights to write (under acknowledgment) to good offices of appointing authority, MD claiming that on Dated.............................Mr/Ms......................designation......................Dept......................in office...................demanded your resignation without explaining the reason and authority to raise such demand.
The whims, fancies, perception of the company's employees in HR etc does not matter, it has to communicate clearly in writing the reason for separation.
It is upto you to deal the matter in the manner as deemed fit looking into your priorities in future.
Even after extracting resignation company and its HR may record in your personnel files that you were asked to separate that may affect BGV in future.
It shall be appropriate to consult a Labor Consultant/Service Lawyer before you proceed on your own.