The paired words which PRECEDE and FOLLOW a quotation, as a kind of punctuation, orally representing the words for punctuation marks " ... "
While "Quote ... endquote" appears more logical, it is in fact the word "unquote" which appears at the end of a direct quotation, according to The Merriam-Webster dictionary, and Fowler's Modern English Usage (a British publication). Neither The Merriam-Webster Dictionary nor Fowler's Modern English Usage lists or recognizes the single word "quote" END QUOTE "unquote", but Fowler's Modern English Usage does indicate that "unquote" appears in the Oxford English Dictionary.
A relevant and contemporary example:
There is no such thing as a QUOTE
secret Muslim UNQUOTE
Muslims OPENLY proclaim their Muslim faith when they say in Arabic QUOTE
ash hadu an La illaha ill Allah wa Muhammadan Ras Ullu UNQUOTE
. To deny or hide their faith is rather QUOTE
not to be a Muslim UNQUOTE
The widely used expression "Quote Unquote"
is a colloquial expression which does not justify its incorrect use in that form, since the two words should be separated by some kind of word, phrase or sentence, a quotation, but is evidence that language is constantly evolving, as with the word "gay", whose primary meaning today is totally different than it was 50 years ago.