That movie is particular/particularly favorite of mine.

Which is correct?

You need to learn to find the answer to such questions by yourself.
Make the Google engine
search over the New York Times site by with:
site:nytimes.com "particular favorite of"
site:nytimes.com "particularly favorite of"
Yes, I should've done it myself first

I got it. I thought the word order was adverb + adjective first, but these are an adjective and a noun phraze, I suppose.

By the way, 'favorite' is countable, so;

These are particular favorites of mine.

Is this correct?
Teachers: We supply a list of EFL job vacancies
Yes, this is correct.
Yes, exactly. Favorite is the countable noun.

It's a particular favorite; they are particular favorites.
Got it! Thanks, GG.
Students: We have free audio pronunciation exercises.
Thank you so much, Marius.