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Aérospatiale-Socata built a prototype of the TB-31 for the French Air Force, which never went to production:
Source: netAirspace.com, photo by miamiair
What is the purpose of the winglets at the top of the vertical stabilizer?
What you observe here are VHF nav antennas for a VOR receiver. This antenna design is lower drag than wire whip antennas.
The antenna serves no aerodynamic purpose except to minimize its own drag profile.
Required, but never shown