In EU institutions, there is no nationality quota for Member State citizens, however, there is a clause in the Staff Regulations requiring "proportional representation".
This means that each Directorate General has 'guiding rates' on the nationality of its staff and aims to recruit new officials to create a geographical balance among the staff and to reflect European civil service values which respects rich cultural and linguistic diversity.
There is no gender quota either, but the new Human Resources Strategy aims to have more women in management positions to achieve more gender balance.
See also:
Staff Regulations | Directorate General
Related links:
Recruitment | Notice of Competition