I've found some sheet music whose key signature simultaneously has:
- Bb (with the round of the b facing left)
- F# (with only one vertical bar instead of two - the left one)

Do these mean something specific ? a different tuning system ?

these are in some Turkish military band music (Mehter) that is also the theme of the heavy-metal piece "Moondance" by Nightwish. Both the Mehter recordings I've listened live in Istanbul and seen on YouTube sound 'occidental' enough in pitches - i.e. an usual scale that doesn't sound "off" on a regular keyboard.