The morphology of articles is entirely a matter of phonology (i.e, sound). It's very simple and completely general.
The indefinite article allomorph a is used before a consonant, and an is used before a vowel; similarly, the definite article allomorph /ðə/ is used before a consonant, while /ði/ is used before a vowel. Whatever sound follows the article determines the allomorphy; never mind whether it's what the article modifies. And since consonants and vowels are the only two kinds of speech sound, this exhausts all possibilities.
Parenthetical words therefore fall under the rules; everything falls under the rules. So, since quote /kwot/ starts with a consonant /k/, an indefinite article preceding it should be a.
(The terms "vowel" and "consonant", by the way, refer only to spoken vowels and consonants, not written ones; that's why an hour and a useful tool are correct, while *a hour and *an useful tool are incorrect.)