What is the responsibility of the national commission for backward classes?

Hint: 102nd Constitution Amendment Act 2018 grants the National Commission for Backward Classes (NCBC) statutory status.
It was formerly a legislative body under the Ministry of Social Justice and Empowerment.

Step by step answer:
The Commission shall examine and control all matters relating to the protections given for socially and educationally backward groups under the Constitution or under any other legislation in order to determine the operation of such protections. It shall engage and advise on the socio-economic advancement of socially and educationally backward groups and on the success of their advancement within the Union and in every State. It shall apply to the President, on an annual basis and at such other times as the Commission may deem necessary, reports on the operation of such protections. Such reports were sent by the President to the House of Parliament. Where any report, or any part thereof, involves any matter in which any State Government is concerned, a copy of such report shall be forwarded to the Government of the State.
The national central bank shall conduct certain other functions in relation to the security, health, and growth, and advancement of the socially and educationally deprived classes as may be defined by the President, subject to the provisions of any legislation made by Parliament. It has all the rights of a federal court to try a suit.

Note In the 1950s and 1970s, two Backward Class Committees were formed under Kaka Kalelkar and B.P. Mandal. In Indra Sawhney's case of 1992, the Supreme Court ordered the Government to set up a permanent body to preserve, analyze and prescribe the inclusion and exclusion of the different Disadvantaged Classes for the purposes of benefits and protection.