The Subsidiary Bank of State Bank of India (SBI) is constituted under the provisions of the State Bank of India (Subsidiary Banks) Act, 1959. This Act was enacted by the Parliament of India to provide for the acquisition of certain banks by the State Bank of India and to define the powers and functions of these banks as subsidiaries of SBI.

Under this Act, SBI is authorized to acquire, establish, and maintain subsidiaries for the purpose of carrying on banking or other related business in India or outside India. The Act defines "subsidiary bank" as any bank in which not less than 51% of the share capital is held by SBI or by its subsidiary companies.

The Act further provides for the transfer of the undertaking of the subsidiary banks to SBI, which includes all assets, liabilities, and business of such banks. The subsidiary banks are also required to comply with the provisions of the State Bank of India Act, 1955, and any other laws that may be applicable to them.

The subsidiary banks of SBI that are currently in operation include State Bank of Bikaner and Jaipur, State Bank of Hyderabad, State Bank of Mysore, State Bank of Patiala, and State Bank of Travancore. These banks operate as separate entities with their own Board of Directors, but are ultimately controlled by SBI.

The subsidiary banks of SBI are subject to the same regulatory framework as SBI, and are required to adhere to the guidelines and regulations issued by the Reserve Bank of India (RBI). The RBI exercises regulatory oversight over these banks, and is responsible for monitoring their financial stability and compliance with applicable laws and regulations.

In conclusion, the Subsidiary Bank of State Bank of India is constituted under the provisions of the State Bank of India (Subsidiary Banks) Act, 1959. This Act provides for the acquisition, establishment, and maintenance of subsidiary banks by SBI, and defines their powers and functions as subsidiaries of SBI. The subsidiary banks are subject to the same regulatory framework as SBI, and are required to comply with applicable laws and regulations, including those issued by the RBI.