Some diacritics and special characters (like ligatures) are accepted in Contemporary English: https://en.wikipedia.org/wiki/English_terms_with_diacritical_marks
Examples of English spellings: coöperative, reëlect, naïve, soupçon, frappé, piñata, Geiger–Müller, Wilhelm Röntgen, László Bíró, …
Some others aren't accepted and wouldn't be used in any publication for an English spelling.
Examples of characters never used in English words: ⱥ, Ω, あ, …
What are the lists of characters with diacritics or special characters (like ligatures) accepted in Contemporary English words?
Question is narrowed to reference organisms or major publications, as:
- Universities, Academic publications
Question does not include:
- anything non-Contemporary, i.e. older than October 6, 1960 (American Standards Association's first meeting to create ASCII)
- non Latin/Roman characters, as you would perform romanization on it to make it an English spelling
- symbols (Ƭ̵̬̊) or emojis (😂, Oxford Dictionaries 2015 Word of the year)
- fiction publications, blogs
Example possible partial list of accepted characters based on Wikipedia article above, would be (in lowercase mostly): äëïöüáóíéèàìôēāăŏčšřžåçșñďľňťŁđćĦ