On the show and in press photos for Castle Rock, The Kid appears to have heterochromia, or two different-colored eyes. This wouldn't be all that notable, except that Bill Skarsgård does not have the condition in real life, meaning it was a deliberate choice to give the character one brown eye and one blue eye. Why?
This might correspond with another theory floating around. What if the real Henry Deaver is trapped inside of The Kid's body? Think about it: The Kid turned up around the time Henry went missing. We never see exactly what happened when Dale Lacy "captured" the boy. We only hear about it when Alan Pangborn talks to Shawshank's new warden: "[Lacy] said he'd always thought the devil was just a metaphor, but now he knew the devil was a boy. And old Dale said he'd caught him and locked the devil in a box. And from here on out it was blue skies and butterflies."
The word choice there is significant to this theory. Pangborn says "a box" instead of "a cage." If you recall, in episode four, when Henry visits the home of Vince Desjardins -- a suspect in his disappearance case -- he finds a literal box behind the house where it looks like a child may have been imprisoned.
If we put all of these clues together, it's possible that Lacy and Matthew Deaver somehow learned that young Henry was the devil incarnate, and staged a kidnapping. In order to prevent town panic in the event of the boy's death, they figured out how to transfer his soul into another vessel: The Kid, who, in this scenario, is either an unlucky Shawshank prisoner ripe for experimentation, or some other low-life person they weren't afraid to sacrifice. They then imprisoned him deep in the bowels of Shawshank Prison, and let the devil-less Henry free. Something went wrong with Matthew -- maybe whatever process was used to make the transfer had a toll on his body -- and he died, and Lacy had to live with the guilt. Perhaps this is why he eventually killed himself, and his last words to The Kid were to ask for Henry Deaver when he was discovered.
This doesn't totally explain the character's "mythological connection" to another King work, but maybe The Kid before all of this happened is someone we know, or related to someone we know. Either way, this could explain why Henry and The Kid seem to share memories, why The Kid's eyes are two different colors (a representation of someone else inside of him), why The Kid seems trapped in a childlike state, and why the bad events in Castle Rock started up again when Henry came back to town. If the part of him in The Kid is put back in his body, all hell could be unleashed.