Star Trek Fic Finder

I may be mixing more than one story but I remember Spock being surprised when a member of the Vulcan High Council is beamed aboard with his adult son, who appears to be human (possibly during the evacuation before the planet was destroyed).

Kirk now goes by another name and IIRC, stayed on the Vulcan ship when he was rescued from Tarsus). He was adopted by either the ship's captain or doctor who discovered Jim had been abused by Frank and abandoned by Winona, and reached out to Sarek to find a loophole in the law that forbids returning a child to a known abusive situation and so avoid notifying Winona that Jim had been on Tarsus and survived.

He grew up shipboard and eventually became the first officer, and eventually graduated from the VSA. Now he works as his father's aide and while he can appear more Vulcan than the Vulcans when necessary, Spock is jealous of the affection and emotional support Jim's Vulcan parent freely displays toward Jim. When I think Spock or Sarek questioned the father, they're told that affection and touch are vital for humans to thrive and he would have been a poor father to knowingly adopt a human child without being willing to ensure his well-being.