If you are abbreviating a word in a document, and that same word shows up in a citation that is NOT a quote, should/can you abbreviate it? My thought is yes. Does it matter if it is a quote?
If the citation is not a quote, then it's your own words (you're paraphrasing), so you can do whatever you like. Making it consistent with the rest of your writing seems appropriate.
If the citation is a quote, you normally report it verbatim. However, minor elisions and edits can be made, so long as you put them in [...]. So if the quote used a verbose phrase, which you've been abbreviating, I think it would be acceptable to replace it with [abbreviation].
If this is a scholarly article being submitted to a journal, you would do best to ask the journal editors what their preferred style is.