1.) To cause fearful distrust of others or a sense of threatened safety, which may be delusional, irrational, or just out of proportion to the situation. (i.e. paranoia)
2.) To rouse excessive suspicion.
Let's look at an example of Chuck the combat vet, and his buddy Josh, who unintentionally PARANNOYS him all the time.
(Chuck jumps, gun poised, as Josh stops by with beer.)
Josh: "Dude, chill, it's just me! I think the Iraq war really PARANNOYED you!"
Chuck: "Yeah, man, since I've been back, it's extremely PARANNOYING whenever someone just shows up unexpectedly like that."
(Josh drops the 6 pack on the floor. (*Loud Crash*)
Chuck: "For F's sake! Will you stop PARANNOYING me?!!"