Every institution in India is bound to operate based on the statutes prevailing in India. Therefore, your institution, even if it is a private concern, has to operate according to such legislation and its provisions. This includes normal working hours, one weekly day off with pay, lunch breaks, entitlement to National & Festival Holidays as per relevant statutes, and the disbursement of wages.
As per your communication, your management must provide a weekly day off with pay, to be mutually agreed upon and then documented with the Appropriate Authorities of the Labour & Rehabilitation Department, which holds jurisdiction in your area. This officer is the legal authority primarily responsible for labor matters in your region.
If your management is not responsive to addressing your grievances, you should seek assistance from the respective chapter of the Institute of Chartered Accountants of India, with which your management is associated. This institution upholds discipline among its members and cannot issue any directives that violate rules and regulations.
All efforts should be channeled through the proper channels, please take note of this.
Best of luck,
Regards