Notice period/ resignation

First of all you identify your problem before seeking solutions or relief to your problem.

Your question seems like a examination question paper,  having no head and tail.

You were given the employment offer letter with the conditions of employment including the terms for resignation and full and final payment at the time of joing the company.

Hence you may peruse the offer letter and find out if you are required to act on the basis of the employer's dictates if the same are not mentioned in the employment offer letter.

You are not bound to comply with the conditions that are missing in the employment offer letter and you can always object and refuse to accept the oral conditions or any other new conditions imposed at the time of resignation.

No offer letter is given

Also salary is paid in cash only

I don't hve anything in writing and don't have and proof for joining nd resigning 

If you have not signed any offer letter neither there's any evidence for your employment how can you prove that you were employed in that company?

A vague query.

Incomplete facts vis-a-vis vague query for consideration and obligation of experts.

If you have some legal dispute / problem/ issue, it is better to consult a local prudent lawyer for proper appreciation of facts, professional advise and necessary proceeding.