So, the old Invention No. 1 by JSB:
The B on the 4th beat of the 1st bar has a [lower] mordent.
I thought it had to be realized like this:
However, almost all recorded performances I can find start with a C, not unlike a trill:
EDIT: Darren has pointed out correctly that I simply have a different edition - the Czerny one.
I checked with a more recent edition and boom: there are trills in there. I should have thought of it.
However, I wonder if Czerny wanted the player to exert his historical knowledge or if he meant those mordents to be played verbatim. His fingerings make me suspect the latter is true.