Is there a word that would refer to a number or a letter, but not any other character (like a comma or an exclamation mark)?
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An alphanumeric character is one which is either alphabetic or numeric — that is, either a letter or a digit. As a noun, we can talk about alphanumerics for the collection of them, as I do here in this answer.
The term alphanumeric does not include punctuation, symbols, combining characters (like diacritics), spacing characters, or control characters.