oooh okay let's see. going down just a list of the cast
google definition is "An unrealistic distrust of others or a feeling of being persecuted." i'm going to think slightly more generally for this, to also mention intense anxiety or obsession

oz: low paranoia (northie worldview); medium anxiety - in the sense that he's low anxiety in general (if he wants something to happen, he'll just make it happen. if he genuinely doesn't want something to happen, he won't do it.), but very high anxiety about arthur's wellbeing, so it balances out to medium
arthur: changing my initial answer after doing heath's section i think she has a lot of anxiety about her relationship to oz and a constant awareness of her position as royalty. i don't think it verges on paranoia, or at least if it does i can't think of an instance of it. she does have that central jealousy tho
cain: a constant buzz of anxiety/obsession that he isn't fully aware of - about losing his station, about letting harm come to arthur or others he cares about, about not being the most important person to the people he wants to be the most important to. his bizarre injury adds fuel to the fire here
riquet: paranoia may not be the right word, but high anxiety & obsession over doing the Right Thing and guiding people correctly. there are moments where i think it bleeds into paranoia (e.g. anni2)

snow: oough i'm not a twins scholar. but i think so? anxiety about losing white again, maybe paranoia about having to maintain the twins' legacy and power as the living twin. the twins take their role as powerful benefactors of the north seriously, as evidenced by what they're willing to do to maintain it/remove any threats, which i think could verge on paranoia
white: he's already dead, so idk. he has that persistent worry that he's not the same white due to being created by snow, but idk if that's a paranoia
mithra: seems too blunted/distanced from emotion to feel much paranoia, but there are moments where she gets paranoid - particularly around the flores siblings doing dangerous things as if they're personally trying to get rid of mithra's magic
owen: like, yes, and no. yes, in the sense that surviving in the north includes a certain amount of being on guard and assuming others have ill intentions, and he carries that worldview into situations where it's not accurate. but no in the sense that owen doesn't seem to harbor false beliefs about others
bradley: similar to owen where northern worldview includes some suspicion of others, but otherwise no

faust: absolutely. it's like in his basic character profile. i do think it's decreased a little since moving into the manor and finding security in his role as the eastern teacher and among his comrades, but i think starting from alec's betrayal up until roughly current point in canon, he harbors deep suspicion and mistrust toward everyone, especially humans. in the way that northies have some mistrust of others baked in, i think easties do as well, but faust's stems from a personal thing
shino: in the way that easties do, he is suspicious/mistrustful of others. in shino's case, it's also because of his upbringing, where he was treated poorly and without care. however, i don't think it bothers him very often; it's just part of how he sees the world
heath: absolutely. same eastie feeling where it's part eastern worldview and part personal experience. in heath's case, there's also her noble upbringing and having to be so aware of how her actions could reflect on her parents. so a LOT of anxiety. i think a lot of the paranoia type things surface around shino, worrying shino isn't loyal to her or that shino doesn't value her the way she wants. she tries to keep these parts controlled, but then they burst out subconsciously. it makes her bizarre injury more interesting, because it manifests a stronger ability to protect herself against things she sees as threats
nero: similar eastie thing of mistrust of others from being eastern and personal experience, AND northie thing of mistrust of others. in nero's case i imagine he spent a century checking over his shoulder in a panic, worried brad and his gang would be after him, and/or that someone in the city of rain would find out he's a wizard and expose him. and he's an anxious person in general, so i think it can verge into being unreasonable/irrational at times

shy: no paranoia or anxiety. some obsessiveness/possessiveness toward murr, but i think he's normal. like some mistrust of humans but in a normal way
murr: current murr, no. past murr, maybe - to the tune of mad genius, or to the tune of "some guy destroyed all my work so now i'm going to divide and hide my new labs and devise tons of traps and seals and disguises so no one can find them again"
chloe: some mistrust of others from his upbringing, and definitely a mistrust toward humans... and some obsessiveness around rustica, and like, being a nice person? i think if pushed/under high stress he could become more paranoid; it helps that he's around rustica and the other westies who keep him safe and encourage him more positively
rustica: no. he's literally just chilling

figaro: yyyyyyes? in the northie way, and in particular due to her history of repeated perceived abandonments. i think she's on constant alert for being abandoned again, which causes her to hold people at a distance or cut ties from her side quickly. and i think, with the aspect of paranoia that's a feeling of being persecuted, figaro struggles to see when she's hurt others because her own feelings are overwhelming and front of mind. tho idk if that counts toward paranoia or just, like, #figaro. oh also specific anxiety around raising mitile due to the prophecy
rutile: no. altho ms2 revealed he has some anxiety under the surface
leno: no paranoia, but a lot of anxiety and obsession around faust
mitile: yes - informed by past experience, but to an unrealistic degree. he has some anxiety/obsession around being "good" and not being like those bad northies, and around being powerful and useful, and around being connected to tiletta