Is this specifically related to the JSS SDK, or is this a general question of how to create an MVC controller in Sitecore for use with AJAX calls?
In either case, how are you registering the Controller route? The one tricky aspect with Sitecore is that you need to register the route in the Sitecore *initialize* pipeline, not in Global.asax. See the documentation below.
If this isn't the problem, please share more information on how you're currently registering your route.