The current possibilities:
1) The "Ace" of the Beast Pirates (New character)
He could be a youngster or some kind of heir, always in hidance and protected by Kaido (explaining why he sticks on his location on Onigashima and doesn't personally leave to expand anymore. This would make it a long term mystery revolving around Kaido's past. The "Prince"!
2) A cildren of Big Mom and Kaido!
A hot take from back then was that the big Triplets (Kata, Oven and Daifuku) are Kaido's sons. Daifuku right now is with Linlin, this could be the moment Daifuku has to present himself. The vibes of Linlin dressing herself up gives me a vibe that she does it for Kaido to bring back old feelings of their relationship. Daifuku is aware of it and is now pressured into the role of a "Prince". The "Prince" theme fits his 1001 Nights theme with the Djinn powers. He would take the "Prince" role.
3a) Toddler Theory!
It is either a Toddler or a young Child (around the age of 8, Oda likes that number for some reasons lel). This would make the child of Kaido a hyper potent enemy for Momonosuke. A future match up or some big plot around it.
3b) The Dragon DNA!
Kaido ask about Momonosuke who was planned to be kidnapped from the start. He refers to him as "Son" because the fruit he ate is related to Kaido's fruit, probably due to some secret Vegapunk experiments while Kaido was captured once.
Momonosuke will get some big secrets about Kaido revealed as some kind of "opening up".