Per Apache Sling, there are different ways to register a servlet path. If you want at first level then you have to register a servlet as '/feed.servlet' and then in 'Apache Sling Servlet/Script Resolver and Error Handler' configuration add '/feed.servlet' as your servlet execution path. Note that '.servlet' is expected and mandatory for first level servlet. If you want to keep at second/more than one level then in the configuration, you have to specify the sub-tree like '/feed/' which will expect a servlet at any of the /feed/ sub-tree e.g. '/feed/fetchData' or '/feed/postData'
If you have given path as '/feed' or '/feed/' in configuration and calling the servlet with http://localhost:4502/feed , it won't work because Apache Sling expects a resource in this case and not a servlet execution script. A servlet script will only be executed in above two scenarios I mentioned.
It seems like you want to add some sugar coat your Sling Servlet Resolver script/path. Please check out this article where it will provide a solution on how you can write endpoints/paths in a more controlled way. It will reveal to you a strategy to hide all the extensions, selectors, paths, etc by doing this the Apache Rewriter Flag.