What is the version of Superdesk you are running? You can see it if you click on the hamburger menu to open the left sidebar, at the bottom of it you will see a "About Superdesk" link, click on it and you will see a modal. In there you can see the version. We need to know that in order to help you out with the API.
But first of all, in order to authenticate as a valid client, you need to create a Subscriber. In Superdesk you can do that by going to the Settings page, in there you will see the option Publish. Once on that view, click on "Add new subscriber". Fill only in the minimum fields, the important part is the API token. When adding the new subscriber, you will see a "Content API Tokens" within the modal window, open it to generate a token. Use the token as indicated here http://docs.superdeskcontentapi.apiary.io/#introduction/authentication and you will then be able to work with the API.
I assume your mail server is an IMAP server, is it configured to allow an application like Superdesk to connect as a client or does it restrict to certain specific client or application?
Also, check the Ingest Dashboard for the corresponding Email source and see if you are getting any errors in the log.