Serving as a branch manager without offer letter - company appointed me orally

DEAR SIR, I am working as a Branch Manager in a private limited company, since Feb 2020. I am working as a casual employee to date. The company appointed me orally. they did not give any offer letter to me nor confirmation of my post. kindly advice.

That means there is nothing binding either on you or the establishment. So long as you are getting salary, it is OK for the present. Maybe once the pandemic situation eases, you can get some documentary reference. Since it is more than a year you are working like this, you may start putting pressure on them.