This character is a member of the Kirk family.

James Kirk was the eldest son of Tiberius Kirk, and brother of George Samuel Kirk, Sr. Kirk's nephew was the legendary James T. Kirk of Starfleet. (TOS novelization: Star Trek: The Motion Picture)

His paternal grandfather was Samuel Abraham Kirk, who served as the ship's historian aboard the USS Pioneer, one of the first Federation Starfleet vessels, in the 2160s. And his paternal grandmother is Valeria Messalina Williams-Kirk whom served under Captain Malcolm Reed's command on the USS Pioneer as the armory officer. (ENT - Rise of the Federation novel: A Choice of Futures)

In Star Trek Generations, in his Nexus experience James T. Kirk finds himself at "his uncle's farm in Idaho", where he met Antonia while riding. It is unspecified whether that uncle was James Kirk, or if it was a brother of his mother.