I don't like that you're thinking of your Green Cheek as being "a mean bird", because that's just not at all true, and it's extremely important that you think of this in a totally different way if you ever want to form a close bond with him, because if you keep thinking of his current behavior as "meanness", then you're not understanding what is actually going on, and if you don't understand what is actually going on then you'll never be able to overcome this or form any kind of relationship with him...So the first thing you need to do is to stop thinking of your bird or his current behavior/personality as being "mean", but rather start thinking of him as being a young bird that was not hand-raised or given much human interaction at all after he weaned by his breeder (which is absolutely not his fault at all), and who is simply scared of people because he's not used to being with them or having much at all to do with them...Then you need to "Hit the Reset-Button" and when you wake-up tomorrow treat it like you just picked him up and brought him home.
It's not at all uncommon (unfortunately) for a young parrot to be sold as "hand-raised" or "hand-fed" by a breeder, to pay the average price that a hand-raised baby parrot costs, and then to find out that your new baby bird doesn't like hands or attention from people in-general...It's due to one of a few possible reasons: #1) The breeder could have just completely lied to you and the bird was actually "parent-raised" but they sold him to you as "hand-raised". This unfortunately happens every day, especially if you bought him from a "breeder" (and I'm using that term loosely) on Craigslist, or if you bought him from a big-box pet shop such as Petco, where they label ALL of their Green cheek Conures, Sun Conures, Jenday Conures, and Black-Capped Conures as "Hand-Fed". Notice the description tags on their cages do say "Hand-Fed", not "hand-raised", and that's how Petco gets away with charging $449 for a Green Cheek Conure that is seemingly wild and not hand-tame at all..."Hand-Fed" simply means that the vendor that Petco buys their birds from pulls their babies from the nest-box by 3 weeks old, but then they put the babies into huge Brooders that hold dozens and dozens of babies at one time, and that's where they stay and live until they are weaned onto solid food, and the ONLY human interaction/attention that any of them get is the 30 seconds it takes for them to pick the baby up and stick a crop-needle down into it's crop, fill-up their crop with formula, and then put them back into the huge Brooder. That's it, that's what Petco calls "Hand-Fed" baby birds. They are actually "Tube-Fed" or "Crop-Fed", they aren't handled at all by anyone nor are they paid attention to, as they are mass-breeders who are tube-feeding hundreds of babies on basically an assembly-line, and they don't have time to actually "Hand-Raise" them, which is totally different and is what produces tame, sweet baby birds that love humans...So that's one possibility....Another is that he was hand-raised, but then after he weaned the breeder stopped paying attention to him and didn't handle him much at all between the time he weaned and the time you bought him...This is probably the case if he isn't absolutely "wild" and seems to not be totally terrified by you, but just doesn't want to be touched...
Either way, it's completely possible to hand-tame your Green Cheek, but it's going to take time from you every single day, working with him, sitting near him and talking to him, reading to him, and figuring out what his favorite treats are and using them as Positive-Reinforcement every single time he does something like steps-up for you without biting/nipping...
****The first thing I would do is to make sure that you locate his cage in the "main" room of your home, which is whatever room of your home that you and others who live there spend most of their time when they're at home. Usually this is the living room, family room, TV room, den, etc. You cannot keep a parent-raised or non-tame, non-socialized bird in a "spare bedroom" or "bird room" that is not the room where the people of the house are at when they're home and then expect the non-socialized, non-tame bird to become friendly and like being around people..."Passive-Interaction" with him is going to be just as important as Direct-Contact/Interaction is, so that means that whenever you're watching TV, playing video games, on the computer, reading, talking with friends/family, eating your meals, having visitors over to your home, etc., that he needs to be in the same room with you and the other people who are there, even if people are not paying him direct-attention, just simply being among you, watching you, hearing you, having people constantly walking past his cage, etc. will do wonders to socialize hime and yes, tame him...This is especially true if he was actually hand-raised but was then ignored and not paid attention to after he weaned and before you bought him, because being around as many people as possible every single day will help to re-acclimate him to being around people and will bring a lot of that original socialization with people back for him...Plus, it will keep him from screaming whenever he knows that people are home because he can hear them out in the living room, but he can't see them because he's back in the "bird room"...