"The Irish Beater Quigley swung heavily at a passing Bludger, and hit it as hard as possible toward Krum, who did not duck quickly enough"
-- during the 1994 Quidditch World Cup final (GF8)
Quigley was a Beater on Ireland’s National Team at the 1994 Quidditch World Cup.
Rather than Ireland's exciting final match against Bulgaria, this first Quidditch World Cup attended by Harry Potter is chiefly remembered for the events that took place in the campground after the match had finished (GF9, Pm).
Other canon notes and references
Quigley is from the 12th century Gaelic O'Coigligh, a nickname for an untidy person, or possibly one with long, flowing, hair (Internet Surname Database).
Like the other members of the Irish National Team, Quigley is named for one of J.K. Rowling's friends:
"The Irish Quidditch team players are all named after people I have known. 'Moran', 'Troy' and 'Quigley,' are good friends." (JKR)