I have heard of six being scored in extra time in the FA Cup fixture Leyton Orient v Droylesden, Orient scoring all six in winning 8 - 2.This
took place on 7 December 2010.
There is a match report on the BBC: BBC NEWS
sports.stackexchange.com/users/949/Thomas
Arsenal and reading 4 goals in overtime isn't a new record.
Most goals scored in extra time in FIFA World cup
was 5 goals in the match between Italy vs West Germany on 1970.
Youtube
I couldn't find any match with more than 5 goals scored in extra time..
sports.stackexchange.com/users/385/Dor Cohen
Late reply, but I found a match with 7 goals in extra time: DFB Pokal (German Cup) , 1974-10-26, between Viktoria Köln and TSG Usingen - from 0-0 to 6-1 ( link , link ).
sports.stackexchange.com/users/9770/NiSch
I saw a thread in Tony's Nonleague Matters forum mentioning two more matches with 6 goals in extra time: 2006 Welsh Cup between Queens Park and Brymbo - from 2-2 to 3-7 ( link ) 1995 FA Cup tie between Walsall and Torquay - from 3-3 to 8-4 ( link )
sports.stackexchange.com/users/1406/Daniel Daranas
In Coupe Gambardella ( U19 Men's French cup ); [round of 64 and round of 32] 12 goals in extra time: Douai SC-Amiens SC: 0-0 to 0-12 Coupe Gambardella 1998-99 10 goals in extra time: Besançon RC-Olympique Lyon: 0-0 to 0-10 Coupe Gambardella 1996-97 In Coupe des Dames 2017-18 ( Luxembourg Women's cup ) [round of 32] 11 goals in extra time: Union Mertert Wasserbillig-Aspelt Remich Bous Entente: 1-1 to 7-6 Soccerway In UEFA Women's Champions League 2017-18 [Final] 5 goals in extra time: VFL Wolfsburg-Olympique Lyon: 0-0 to 1-4 UEFA
I also saw a match with 7 goals in overtime in the Coupe de France (French Cup) in round of 512
but I can not find the match in question.
sports.stackexchange.com/users/15384/Danyss77nfs
In German Central Rhine Regional Cup 2020 [quarter-finals] 6 goals in extra time: Germania Windeck - Viktoria Arnoldsweiler 0:0
to 0:6 kicker
sports.stackexchange.com/users/20004/Stanley
On 30-Oct-2012,  Arsenal defeated Reading  with an incredible score of 7-5. A more astonishing fact is that 4 goals were scored in Extra-time.  Is this the record for the most number of goals in extra-time, in a single game? If not, which match holds the record?
Most number of extra-time Goals
sports.stackexchange.com
<football><history><records><statistics><trivia>
sports.stackexchange.com/questions/1784
sports.stackexchange.com/users/857/Orangecrush
From the evidence, it appears that 12 is the highest number of goals scored in extra time. That was in  the Coupe Gambardella  ( U19 Men's French cup ); [round of 64 and round of 32]  12 goals  in extra time: Douai SC-Amiens SC: 0-0 to  0-12. There are conflicting views on the maximum number of extra-time goals. Answers vary from 6 to 12, where France holds the record.
There are conflicting views on the maximum number of extra-time goals. Answers vary from 6 to 12, where France holds the record.