Question: What fighter-wing pilot was one of the top three scoring flying aces of all time and exceed 300 confirmed victories?

Context paragraphs:
List of Syrian flying aces: The following Syrian pilots became flying aces by scoring five or more confirmed aerial victories while flying combat against the Israeli Air Force.

Josef František: Josef František DFM & Bar (7 October 1914 – 8 October 1940) was a Czech fighter pilot and World War II flying ace who flew for the air forces of Czechoslovakia, Poland, France, and the United Kingdom.  He is famous as being one of the highest scoring Allied aces in the Battle of Britain, although he was killed in a crash in the final weeks of the campaign.  František had 17 confirmed victories and one probable, all gained over a period of four weeks in September 1940.

Karl Emil Schäfer: Karl Emil Schäfer (17 December 1891 – 5 June 1917) was a German pilot during World War I; he became one of the major German flying aces of the war, with 30 confirmed aerial victories.

Philip F. Fullard: Air Commodore Philip Fletcher Fullard {'1': ", '2': ", '3': ", '4': "} (27 May 1897 – 24 April 1984) was an English First World War flying ace, one of the most successful fighter pilots of the Royal Flying Corps, with a reputation as a superb combat leader.  With 40 confirmed victories, he was the top scoring UK ace flying Nieuports, and overall the 6th highest scoring British pilot, and the 2nd highest to survive the war.

Gerhard Barkhorn: Gerhard "Gerd" Barkhorn (20 March 1919 – 8 January 1983) was the second most successful fighter ace of all time after fellow "Luftwaffe" pilot Erich Hartmann, the two people to ever exceed 300 confirmed victories.  Barkhorn joined the "Luftwaffe" in 1937 and completed his training in 1939.

List of World War I aces from Latvia: The list of World War I flying aces from Latvia contains only one name with five confirmed victories, as well as the names of two others whose claims were unconfirmed.

Olavi Puro: Olavi Kauko Puro was born on 18 November 1918 in Helsinki and died on 20 June 1999.  He was one of the top scoring aces in the Finnish Air Force with 36 confirmed victories.

Jagdgeschwader 52: "Jagdgeschwader" 52 (JG 52) (52nd Fighter Wing) of the Luftwaffe, was the most successful fighter-wing of all time, with a claimed total of more than 10,000 victories over enemy aircraft during World War II.  It was the unit of the top three scoring flying aces of all time, Erich Hartmann, Gerhard Barkhorn and Günther Rall.  The unit flew exclusively with the various versions of the Messerschmitt Bf 109 throughout the war.

David Thwaites (flying ace): David F. Thwaites was an aviator in the United States Army Air Corps during World War II.  He became a fighter ace piloting the P-47 Thunderbolt as a member of the 361st Fighter Squadron of the 356th Fighter Group.  Thwaites, based out of RAF Martlesham Heath in England was the second highest scoring pilot in his squadron, with six confirmed victories and the only pilot of the 356th FG to score all of his victories while serving with the group.  He scored his victories using three different P-47s however he nicknamed them all "Polly".  Following the completion of his tour in September 1944 he returned to the United States and became an instructor.

Olli Puhakka: Risto Olli Pekka Puhakka was born on 11 April 1916 in Sortavala and died on January 28, 1989.  He was one of the top scoring aces in the Finnish Air Force with 42 confirmed victories.

Supporting paragraphs: Jagdgeschwader 52 Gerhard Barkhorn
Answer: Gerhard Barkhorn