The correctly spelled word is "appellation". It is a noun that means a name or title, especially one that is given officially or formally. For example, "the appellation of the king" or "the appellation of the university".
The other options are incorrect spellings of the word "appellation". "Apallation" is a misspelling that is likely due to a typo. "Appellant" is a noun that means a person who makes an appeal, especially in a court of law. "Appallation" is a noun that means a feeling of shock or dismay.
