What is the ruling on erroneous beliefs that come to a person's mind, and then he regrets them?

These thoughts are from the whisperings of Satan. You should turn away from them and occupy your time and mind with learning, inviting to Allah, exercising, and permissible recreation. Your fear and regret are proof of the purity of your faith, for "that is clear faith," as stated in the Muslim hadith (definition). Fleeting thoughts and self-talk are forgiven as long as one does not dwell on them, for "Allah has forgiven my nation for what they talk about to themselves, as long as they do not speak of it or act upon it." Whoever experiences thoughts of disbelief as mere fleeting notions and immediately dismisses them is not a disbeliever and is blameless.