
They'd be 18 at the oldest now, but that depends on when their birthdays are. If Shin was too young for the King to bed him, he had to have been 14 at oldest.
Then in the new chapter, 4th Prince mentions to Sys that talk he had with 3rd Prince three years ago.
I have no idea about Shin's banishment though.

He slaughtered men, women, the elderly, and children back at the hospital during Sys' childhood because they stood up for Sys' parents who treated the Miller's son who attempted suicide with a snake bite to escape the King. My guess is his 15th birthday was approaching. The miller's son essentially doomed them all to death to save himself from the King's wrath, only to accepted his fate in the chamber of bloom.
From what I gather, Shin is not in the children's quarters anymore, he is banished from the palace, but somewhere nearby and probably under watch. The King has not come to see him since his punishment a few years ago, but he and Sys are always prepared. Shin was also the King's favorite - so while he couldn't stand the idea of Shin being tainted by someone else, I don't think he could kill him after the death of the first black haired boy. Plus he's also the son of a minister, so I think that killing Shin would have been too dangerous a move for him politically.
Sys' parents, the poor, the elderly, and children of lesser standing are all free game for the King though. Thanks to his corrupt ministers, there's no repercussion for enslaving, starving, and killing the powerless. The ministers can afford to send their children away their children until they reach adulthood. So long as the King's actions don't threaten them, they don't care about the kingdom.

Now that makes sense. Thanks! And I just want to say that that kid in the hospital? *breathes* HE'S A JERK!! GOD! I WISH SYS DIDNT CURE HIM! HE SHOULD HAVE DIED FROM THE POISON INSTEAD!! THE POOR VILLAGERS DIDNT DESERVE THAT KIND OF DEATH! AND JUST BECAUSE OF HIS LIES!!!!???
JUSTICE FOR SYS' PARENTS! (☄◣д◢)☄

Maybe you're right but it still dosen't makes total sense to me. The first panel of chapter 26 show the same building as the chapter 29 where it's cleary described as the children's quarter. And, to me, the king doesn't seem to care or be worried about any other ranks or political figures (If the ministers and nobles needs to send their kids away until 15 to protect them...). Maybe he did spare Shin because he was his favorite, but it's not very well conveyed in this case. (and he seemed more like the kind of guy to make him suffer extra for the very personal betrayal... emotional jerk !)
But maybe I'm getting ahead of myself here and it will all be explained later ! I think the time jump being immediatly cut by Sys flashback kinda threw me off... ;)

I agree it doesn't make sense - why would someone he banished still be in the children's quarters? The whole thing isn't very well explained or resolved, we're given no explanation.
If you're right, that's why our...
*SPOILERS*
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Lovebirds meet up next chapter! So maybe that's why they couldn't speak and had to use Sys to exchange messages? He couldn't leave the children's quarters, despite his banishment that isn't a banishment? But now that Sys showed him the secret way in they can meet up? I dunno. Shin's current situation makes no sense from a writing standpoint without clarification. I really hope they explain why things are the way they are.
I'm not sure I understood everything. Why is Shin still in the children's quarters ? Wasn't he supposed to be banished for "cheating" on the King ? What was his punishement exactly ? Was it just to be paraded naked in front of the crowd ? It seem too magnanimous for that monstruous King. And how long was the time jump ? Isn't Shin too old for the King, now ? (Yuck...)
Why am I the only one so confused ? (⊙…⊙ )
(Sorry...)