I went over this table of Fields Medal winners [1] and the 4n+2 people have won 28% of the awards. However, 33% of the awards were won by 4n+3 people but only 17% were won by 4n+0 people.

So your hypothesis does seem to bear out: people born on 4n+0 years are at a significant disadvantage for winning a Fields medal.

[1] https://stats.areppim.com/listes/list_fieldsxmedal.htm