For a Green Cheek Conure, yeah, your cage is way too small, I agree with Monica...I don't know where you got the "recommended size", but the larger the cage the better. Always buy the largest cage you can afford, and with a Green Cheek who loves to climb and play with a TON of toys, your cage is not at all adequate. And that isn't your fault, for example, Petco sells a table-top cage that is labeled "Conure Cage"...it's the size of a Budgie cage, lol...They also sell a floor-cage that is labeled "Conure Cage", and it's 4-times the size of their table-top "Conure Cage"...so how does that work Petco?
Not only the size of the cage, but also, as already mentioned wisely by Jen, is the LOCATION OF HIS CAGE...Where do you have his cage located? If the situation is that he's screaming while inside his cage when you're home, and his cage is in a different room than where the "action" is in your home (i.e. the room where the people who live in your home spend most of their time when they are home, usually a living room, family room, den, etc.), then that's at least 50% of the problem. Any time your bird is inside of his cage but he cannot see the people who are at home at the same time, this is going to result in screaming. If he can hear you but not SEE you or the others who are home, he's going to go nuts. He wants to be where the people are...and what you'll find, if this is the situation, is that if you move his cage to main room of your house where the people spend their time, and he's simply inside of his cage and in the same room as the people are while they're simply watching TV, playing video games, reading, eating/cooking, etc., your bird will most-likely play happily and silently inside his cage, simply because he's "with his people/family". You don't have to always be directly-interacting with him, but he must always be with his people when they are home, that's just how Conures work...a lot of people find this out because they put their bird's main-cage in their bedroom or a spare-room (often calling it "the bird room" or "bird's room"), thinking that the bird should have it's own room, or be located in their own bedroom because it's "their bird" and not the rest of their family's bird, however, this is exactly what happens, especially with a clingy bird like a Conure...