First of all, it should be QUOTE and ENDQUOTE. These are the official names for the double apostrophe symbols (") on your keyboard.
Secondly, the proper syntax is to say QUOTE, followed by the phrase, closed by ENDQUOTE.
CORRECT USAGE (spoken):
What do you think of Bush's quote War on Terror endquote?
What do you think of Bush's "War on Terror?"
INCORRECT USAGE (spoken):
What do you think of Bush's quote unquote War on Terror?
What do you think of Bush's ""War on Terror?
Get it? Good. But try to avoid saying it altogether. Using the phrase "so-called" is much more acceptable. Example:
What do you think of Bush's so-called War on Terror?
BOSS: Ok people, let's get proactive. This is a win-win situation. So give it 110% and quote unquote kick some ass!
EMPLOYEE: Man, you're such a putz.
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.
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.