Small finance banks are governed by Banking Regulation Act 1949, Reserve Bank of India Act, 1934 and various other acts. Small finance banks can be started after fulfilling the legal and regulatory requirements put forth by RBI.You can read about the Types of Banks in India – Category and Functions of Banks in India in the given link.

The license for small finance banks is provided as per section 22 of Banking Regulation Act 1949. It is registered as a public limited company as per Companies Act of 2013.

Further readings:

1. Granting License for Small Finance Banks by the Reserve Bank of India (RBI)
2. RBI – Reserve Bank of India [UPSC Indian Economy Notes]