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1.
Specifically and emphatically, usually with a contrarian connotation. (Yiddish). Roughly equivalent to the exasperated "don't you think", as in "The plumber said he'd come between 12 and 3, so don't you think he came at 4!"
All the best Christmas songs were davka written by Jews.

Rochelle doesn’t make her house kosher for Passover, so she davka shedules her daughter’s bat mitzvah for the day before Passover, so it should be even more difficult for those of us who do.
by Wicked Son March 31, 2010
 
2.
A Yiddish word used in English by Yiddish speakers or in general speakers of Jewish-influenced English, because there's no precise English equivalent. It is variously translated as unexpectedly, just to spite, despite everything, whaddayaknow, of course, just my luck, in fact, actually... basically it's an adverb which captures the essence of Murphy's Law, "because of course, something HAS to go wrong".

Note:
Davka generally precedes the subject (The one day I get to uni early, and davka my class was cancelled!) but it may also come after the subject (The one day I get to uni early, and I davka left my pen at home!)
I only had time to study the first 3 chapters for the exam, and davka the essay was on chapter 4!

For the whole first hour of the movie I was fine, but now the exciting part starts and I davka need to go to the toilet!

I leave my car for just 5 minutes, and davka I get a parking ticket!
by AndreRD June 04, 2013