Is there a chance to recover my Apple ID that was permanently deleted

Depends on how it was deleted.

If you specifically requested its deletion as explained here: link->How to delete your Apple ID account - Apple Support

Then you have a short period of time to cancel the request and get it back by using the steps and code sent to your email address when you requested the deletion.

When you request account deletion, you'll receive a unique alphanumeric access code. Make sure that you keep this access code in a safe place. For a short period of time while your request is being processed, you can contact Apple Support, provide your access code, and we’ll help you cancel your request so you can resume using your Apple ID. 

If you did something else, then its likely not actually deleted, but you would have to explain what you did for any further advice.

If you deleted an Apple ID there is no way to recover it or any of the content associated with it. See→How to delete your Apple ID account - Apple Support