How do I get current_user in ActionCable rails-5-api app?

If you see the doc you provided, you will know that identified_by is not a method for a Channel instance. It is a method for Actioncable::Connection. From Rails guide for Actioncable Overview, this is how a Connection class looks like:

#app/channels/application_cable/connection.rb
module ApplicationCable
  class Connection < ActionCable::Connection::Base
    identified_by :current_user

    def connect
      self.current_user = find_verified_user
    end

    private
      def find_verified_user
        if current_user = User.find_by(id: cookies.signed[:user_id])
          current_user
        else
          reject_unauthorized_connection
        end
      end
  end
end

As you can see, current_user is not available here. Instead, you have to create a current_user here in connection.

The websocket server doesn't have a session, but it can read the same cookies as the main app. So I guess, you need to save cookie after authentication.

if you are using devise gems in rails, Please replace this function:

def find_verified_user # this checks whether a user is authenticated with devise
  if verified_user = env['warden'].user
    verified_user
  else
    reject_unauthorized_connection
  end
end

I hope this will help you.