The drawings actually serve multiple purposes in the film.
They first and foremost add to the character building of TJ. They show that he is talented and creative and has a hobby that sets him apart from the mass. It adds to his image of a street kid that is intelligent and considerate when compared to the environment he grows up in. In this way it adds to other aspects of his character, like the general smartness, the love for books and hanging around in the library (although that has other reasons, too), the way he cares for a healthy diet. With the hand drawings there's just another layer of uniqueness to him.
But they also serve to channel the friendship between him and Scudder. It is by finding one of his hand drawings that Scudder first comes in contact with him. Later he takes the drawing that TJ leaves at the restaurant and takes it with him. TJ later finds it laying around in Scudder's apartment. This is a way of showing (both to us and to TJ) that Matt cares for the boy to some degree, since he keeps a personal item from him. They both always play cool to each other, but it's clear they are friends and Scudder cares for TJ. While there are other signs that show this, the hand drawing that Matt took with him is just another way.
Last but not least, there's another drawing at the very end of the film. When Matt returns home after all is done and solved, he finds TJ sleeping on his couch and he finds a drawing of a superhero with a sickle emblem on his chest. This relates to TJ's earlier story in the hosptial about him having sickle-cell anaemia (and his mother's explanation of his blood being "special"). So the hero is likely a representation of TJ himself. This shows us that TJ sees himself (and by extension Scudder?) as a hero for helping Matt solve the crime and save the girl. Furthermore this might mean that he has now found a purpose in life (which adds to his general interest in detective work exhibited during the film).