Hi @Sajith Gopalakrishnan Hema ,
You can try to use refinement filters or wild cards in SharePoint search API
Maybe one of the endpoint given below:
_api/search/query?refinementfilters='FirstName:("s*")'
or
http://server/_api/search/query?query_parameter=value*
The document you can refer to
https://learn.microsoft.com/en-us/previous-versions/dynamicsnav-2013r2/hh169248(v=nav.71)?redirectedfrom=MSDN
https://learn.microsoft.com/en-us/sharepoint/dev/general-development/keyword-query-language-kql-syntax-reference
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