A three-part index in which works cited during a given year are listed alphabetically by name of author cited, followed by the names of the citing authors (sources) in a "Citation Index." Full bibliographic information for the citing author is given in a "Source Index." Also provided is a "Subject Index," usually listing articles by significant words in the title. Researchers can use this tool to trace interconnections among authors citing papers on the same topic and to determine the frequency with which a specific work is cited by others, an indication of its significance in the literature of the field.

                       Citation indexing originated in 1961 when Eugene Garfield, Columbia University graduate in chemistry and library science and founder of the fledgling Institute for Scientific Information (ISI), received an NIH grant to produce the experimental Genetics Citation Index, which evolved into the reference serial Science Citation Index. ISI subsequently published Social Sciences Citation Index beginning in 1972 and Arts & Humanities Citation Index from 1978.

                                                     A citation index is a kind of bibliographic index, an index of citations between publications, allowing the user to easily establish which later documents cite which earlier documents. A form of citation index is first found in 12th-century Hebrew religious literature. Legal citation indexes are found in the 18th century and were made popular by citators such as Shepard's Citations (1873). In 1960, Eugene Garfield's Institute for Scientific Information (ISI) introduced the first citation index for papers published in academic journals, first the Science Citation Index (SCI), and later the Social Sciences Citation Index (SSCI) and the Arts and Humanities Citation Index (AHCI). The first automated citation indexing was done by CiteSeer in 1997. Other sources for such data include Google Scholar and Elsevier's Scopus.

Major citation indexing services

Web of Science by Clarivate Analytics (previously the Intellectual Property and Science business of Thomson Reuters)

Scopus by Elsevier, available online only, which similarly combines subject searching with citation browsing and tracking in the sciences and social sciences.

Indian Citation Index is an online citation data which covers peer reviewed journals published from India. It covers major subject areas such as scientific, technical, medical, and social sciences and includes arts and humanities. The citation database is the first of its kind in India.

Each of these offer an index of citations between publications and a mechanism to establish which documents cite which other documents. They differ widely in cost: Web of Science and Scopus are available by subscription (generally to libraries).

In addition, 

1. Microsoft Academic Search
2. Google Scholar
3. Scopus
4. Semantic Scholar
5. Citation analysis
6. Acknowledgment index
7. CiteSeer
8. CiteSeerX
9. Scientific journal
10. Science Citation Index
11. Indian Citation Index
12. Journal Citation Reports
13. Emerging Sources Citation Index (ESCI)
14. SciELO
15. Redalyc
16. Index Copernicus

Reference:

Wikipedia and IGNOU