I'm surprised that kid hasn't surfaced by now. He would be about 33 years old. Also it's interesting that cut scenes in three Trek films (II, III, and IV) all involve children.
Nope, it's cut/unfilmed children scenes in FOUR TOS movies!
The original idea for the Spock flashback in TFF was to hire two younger actors to play Sybok and Spock for the flashback where Sybok leaves Spock behind to follow his own path.
If you listen to the Shatner and his daughter commentary she brings up the fact that they were actively testing young actors for the parts.
For whatever reasons (money, time, creative choice) they instead decided to go with the two older actors pretending
to be their younger selves! Wow, was Nimoy terrible in that deleted scene!
So, children scenes filmed for 2 and 3 cut and scripted scenes for 4 and 5 that never got filmed--wow.
But as they say "try and try again" Star Trek 6 finally got a child into the series as Martia's younger disguise in the escape scene!