I wanted to know what part of speech a letter might be or I wanted to see if I understand letters. Do people ask this question in this place? Or am I in the place where people would ask this? I asked this in language-learning because I thought it would be a language question but I think they showed me that it wasn’t a language question.
There are two answers, depending on what you are asking. First, they are nouns, so they get case, can be subject or object, take determiners etc. If you have a more nuanced theory of POS with subtypes of nouns, it depends on the language and the theory.
The other, which came up in the comments, is about the actual letters, not the names of the graphic symbols. But in addition, linguists now distinguish "letters" and "sounds" (though Rask talked of changes in letters, and Rask was a linguist). If we speak, we make sounds, if we sign, we make "signs" and if we write, we make letters or characters, depending on what language we're writing. Speech is spoken, so there are no letters in speaking. However, "part of speech" is not about speech, despite the name, it is about language, so letters are a part of language. But, "part of speech" doesn't refer to all of the entities that make up language, it refers to a very specific categorization of words, in terms of syntactic criteria. Letters are not classified according to any syntactic criteria, so they don't have a "part of speech", nor do language sounds. "Root", a morphological concept, likewise is a morphological entity, not a syntactic one, so roots don't have a "part of speech".