Howto combine UNION with EXISTS?
The WHERE clause is specific to each individual SELECT so you would need to move the one you have to the first SELECT like this:

SELECT PubKey, Title FROM Publication
WHERE EXISTS (
    SELECT * 
      FROM UserPublication 
     WHERE UserPublication.PubKey = Publication.PubKey
)
UNION
SELECT NoteKey, Title FROM Note


However, if you want to specify the WHERE clause across the entire result set. This must be done like so:

SELECT * FROM (
    SELECT PubKey, Title FROM Publication
    UNION
    SELECT NoteKey, Title FROM Note
) AS A
WHERE EXISTS (
    SELECT * 
      FROM UserPublication 
     WHERE UserPublication.PubKey = A.PubKey
)