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?
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3$\begingroup$ I'd guess those are localizer antenna with an aerodynamic dielectric fairing. Many aircraft are fitted with similar designs $\endgroup$ – Carlo Felicione May 20 '17 at 17:21
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$\begingroup$ They are likely VOR antennas. Many Bonanzas and Cessnas have these as well. The V-tails have them on the fuselage under the V. $\endgroup$ – acpilot May 20 '17 at 18:30
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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.
