David Marcus never knew who his father, James Kirk, was because his mother Carol Marcus didn't want David to join Starfleet and become an officer like his father. He did follow in his mother's footsteps and became a highly respected scientist in his own right. He even helped in the Genesis Project and was eventually killed because of it when Klingons tried to steal it as a weapon.
Davis Marcus was created for the second Star Trek film Star Trek II the Wrath of Khan.
After his death the David Marcus Research Center was created in his name to stop hunger on all planets.