How to handle exceptions with Swagger?

Swagger by itself does not handle application exceptions as yet.

You will either need to create custom Exception classes (that extend java.lang.exception) or use the existing ones (like WebApplicationException that you are already using) and make the API definition throw these errors. So basically you need to use Java/J2EE/Jersey to throw proper exceptions. Swagger UI will display them for you.

Check this link for details on REST exception handling with Spring.