Foreign investment in infrastructure companies in securities markets (e.g. stock and commodity exchanges, depositories and clearing corporations) is allowed up to 49% under the automatic route (without prior government approval). Foreign investment in all 'other financial services' not under the formal supervision of a financial sector regulatory authority and not explicitly addressed in the FDI Policy requires prior approval of the government.
"CHAPTER 3: GENERAL CONDITIONS ON FDI [...]
3.4   ENTRY ROUTES FOR INVESTMENT 3.4.1 Investments can be made by non-residents in the equity shares/fully, compulsorily and mandatorily convertible debentures/fully, compulsorily and mandatorily convertible preference shares of an Indian company, through the Automatic Route or the Government Route. Under the Automatic Route, the non-resident investor or the Indian company does not require any approval from Government of India for the investment. Under the Government Route, prior approval of the Government of India is required. Proposals for foreign investment under Government Route, are considered by respective Administrative Ministry/Department. 
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3.5   CAPS ON INVESTMENTS
3.5.1 Investments can be made by person resident outside India in the capital of a resident entity only to the extent of the percentage of the total capital as specified in the FDI policy. The caps in various sector(s) are detailed in Chapter 5 of this Circular. 
3.6   ENTRY CONDITIONS ON INVESTMENT
3.6.1 Investments by non-residents can be permitted in the capital of a resident entity in certain sectors/activity with entry conditions. Such conditions may include norms for minimum capitalization, lock-in period, etc. The entry conditions in various sectors/activities are detailed in Chapter 5 of this Circular.
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5.2 PERMITTED SECTORS
a) In the following sectors/activities, FDI up to the limit indicated against each sector/activity is allowed, subject to applicable laws/regulations; security and other conditionalities. In sectors/activities not listed below, FDI is permitted up to100% on the automatic route, subject to applicable laws/regulations; security and other conditionalities. [...]
c) Foreign investment in sectors under Government approval route resulting in transfer of ownership and/or control of Indian entities from resident Indian citizens to nonresident entities will be subject to Government approval. Foreign investment in sectors under automatic route but with conditionalities, resulting in transfer of ownership and/or control of Indian entities from resident Indian citizens to non-resident entities, will be subject to compliance of such conditionalities. 
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FINANCIAL SERVICES
Foreign investment in other financial services, other than those indicated below, would require prior approval of the Government.
5.2.17 ASSET RECONSTRUCTION COMPANIES 
5.2.17.1‘Asset Reconstruction Company’ (ARC) means a company registered with the Reserve Bank of India under Section 3 of the Securitisation and Reconstruction of Financial Assets and Enforcement of Security Interest Act, 2002 (SARFAESI Act).  | % of Equity/FDI Cap: 100% | Entry Route: Automatic.
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5.2.20 CREDIT INFORMATION COMPANIES (CIC) 
5.2.20.1 Credit Information Companies  | % of Equity/FDI Cap: 100% | Entry Route: Automatic.
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5.2.21 INFRASTRUCTURE COMPANY IN THE SECURITIES MARKET 
5.2.21.1 Infrastructure companies in Securities Markets, namely, stock exchanges, commodity exchanges, depositories and clearing corporations, in compliance with SEBI Regulations | % of Equity/FDI Cap: 49% | Entry Route: Automatic.
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5.2.25 WHITE LABEL ATM OPERATIONS 
White Label ATM Operations | % of Equity/FDI Cap: 100% | Entry Route: Automatic.
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5.2.26 OTHER FINANCIAL SERVICES
Financial Services activities regulated by financial sector regulators, viz., RBI, SEBI, IRDA, PFRDA, NHB or any other financial sector regulator as may be notified by the Government of India. | % of Equity/FDI Cap: 100% | Entry Route: Automatic.
5.2.26.2 OTHER CONDITIONS
i. Foreign investment in 'Other Financial Services' activities shall be subject to conditionalities, including minimum capitalization norms, as specified by the concerned Regulator/Government Agency. 
ii. ‘Other Financial Services' activities need to be regulated by one of the Financial Sector Regulators. In all such financial services activity which are not regulated by any Financial Sector Regulator or where only part of the financial services activity is regulated or where there is doubt regarding the regulatory oversight, foreign investment up to 100% will be allowed under Government approval route subject to conditions including minimum capitalization as may be decided by the Government.[...]" (Government of India/Ministry of Commerce and Industry (2020), Consolidated FDI Policy (Effective from October 15, 2020))
Government of India/Ministry of Commerce and Industry (2020), Consolidated FDI Policy (Effective from October 15, 2020)
[<a href="https://dpiit.gov.in/sites/default/files/FDI-PolicyCircular-2020-29October2020_0.pdf">Policy</a>]