If you want to get the user data by providing username, you can use pass name
(username) as a parameter to the service URL like follows
http://example.com/<endpoint path>/user?parameters[name]=krishna
If you want to pass either username or other user profile fields you can achieve that using Services Views module. After installing this module make sure to enable it under service resources list.
Create a view with contextual filter(s)
Executing view via views resource
After enabling "views" resource in your services endpoint you can do GET request to:
http://example.com/<endpoint path>/views/<view name>
This will execute a view and pass results.
Possible arguments:
- display_id: views display
- args: array of view arguments
- filters: array of view filter values
- offset: views offset
- limit: limit views number of results
- format_output: boolean whether we would like to get themed view or data