How to set response header in JAX-RS so that user sees download popup for Excel?

You don’t need HttpServletResponse to set a header on the response. You can do it using
javax.ws.rs.core.Response. Just make your method to return Response instead of entity:

return Response.ok(entity).header("Content-Disposition", "attachment; filename=\"" + fileName + "\"").build()

If you still want to use HttpServletResponse you can get it either injected to one of the class fields, or using property, or to method parameter:

@Path("/resource")
class MyResource {

  // one way to get HttpServletResponse
  @Context
  private HttpServletResponse anotherServletResponse;

  // another way
  Response myMethod(@Context HttpServletResponse servletResponse) {
      // ... code
  }
}