A problem, difficulty or nuisance.
A flat tyre on your car is a fasaria unless it is a burst front tyre at 145 kilometers an hour whilst cornering whereupon it may well become a catastrophia since, if you survive, they may well send you to the nosogomieon. (Unless, regrettably, a kliniki gets you first in which case pray hard and tell them you have no insurance - ideally before they administer the anaesthetic)
Another use of the word is embodied in the phrase "tha gano fasaria" or "I am going to make a problem".
A Cypriot confident enough to shout this at you either has a few friends close at hand to "hold him back" whilst he raves of his martial arts/pugilistic prowess or else is much bigger than you are. Alternatively he may be under the influence of locally grown recreational pharmaceuticals. He may or may not shout a few Kung-Fu-esque "Ahhya"'s in an attempt to bluff or intimidate, or even roar "adeh re" for emphasis if he is sober enough to articulate it.
Bearing in mind he will seldom issue this challenge unless he is positive there is no element of personal risk (to him), it is best to leave immediately as this is a pre - kafka posture and may lead to violence once the challenger feels sure enough of himself.