The 17-year-old Yun beat Jeffrey Kang, 3 and 2 in the third round earlier Thursday. He will face 14-year-old Jordan Spieth, who needed a total of 28 holes Thursday to win two matches.
Spieth beat Julian Suri, 4 and 3, in the morning and David Persons, 8 and 7, in the third round.
Fernandez Valdez, a 15-year-old from Argentina, was the medalist with a 36-hole total of 5-under 139 at the 7,251-yard Shoal Creek Golf Club course.
He beat Bobby Wyatt, 3 and 2 in the third round.
Cameron Peck, 17, and Emiliano Grillo, another 15-year-old from Argentina, will meet in another of Fridays quarterfinals, while Andrew Steinhofer, 17, faces Dom Bozzelli, 17, and Evan Beck, 17, goes against Ernesto Marin, 17.
The quarterfinalists are exempt for next years Junior Amateur if they are still 17 or younger.
The 36-hole final is Saturday.