Kaneki, 3 years ago, lost his mind and memories, and he was "reformed" as Haise Sasaki, basically an amnesiac Ken. In game, Kaneki was canon updated, and instead of Sasaki being amnesiac about Kaneki's all of memories, he actually has all of the in game memories Kaneki made. So basically, 2 years worth of memories and feelings were dumped on Sasaki which he is... pretty lost on what to do because. wellp. what now. He is still missing canon memories, but in game memories are all there.
Sasaki is an amnesiac Kaneki, and thus he often gets flashbacks of Kaneki. At first he saw all of that as something REALLY TERRIBLE and fought it, so he had this weird monster (Sasaki's image of Kaneki) inside his head often telling him "give my body back". However, as canon progressed, Sasaki started to learn things about Kaneki and this modified Sasaki's vision of Kaneki. He started to see him as a boy with white hair who doesn't want to be erased. He wants to exist and Sasaki continued to deny him, and that only hurt tiny!Kaneki. So Sasaki decided YOU KNOW WHAT I'M NOT GONNA IGNORE YOU ANYMORE. Right now, Sasaki actually has a tiny!Kaneki inside his mind; they interact and tiny!Kaneki is actually somewhat of an asshole because while Sasaki doesn't want to remember (because if he remembers, he will stop existing and will become Kaneki again), tiny!ken often tells him that Sasaki is just a dream, a parasite, and he has to remember. not cool smol child, not cool.
With in game memories, this smol child got a lot louder. And he is specially present whenever Haise says "i'm not Kaneki, i don't know who you are" and denies all of the memories he does have. smol child doesn't like Sasaki denying it. at all.
Visually speaking, inside Haise's mind, telepaths can see the child. Sasaki hallucinates him on a very regular basis, to the point tiny!ken is just there and he goes along with it. i'd guess that telepaths can also speak to smol!Kaneki because Sasaki speaks to him too. all the time. In a medical sense, smol!Kaneki is just a coping mechanism that Sasaki made up. he isn't the real Kaneki or anything, he is like a representation of what Sasaki wants to deny. basically, Kaneki's memories.