Quark?
No, he wasn't TNG...
But, Barklay was on all three.
Quark appeared on TNG, in the episode Firstborn.
Barclay never appeared on DS9. He was only on TNG and VOY.
The only characters to appear on all three shows were....
1.) Quark - mainly a DS9 character who appeared in TNG: Firstborn and VOY: Caretaker.
2.) Morn - mainly a DS9 character who appeared in TNG: Birthright, Part One and VOY: Caretaker.
3.) Broik - mainly a DS9 character (one of Quark's Ferengi waiters) who appeared in TNG: Birthright, Part One and VOY: Caretaker.
4.) Q - mainly a TNG character who appeared in DS9: Q-Less and VOY: Death Wish, The Q and the Grey, and Q2.
5.) Gul Evek - a character who first appeared in DS9: Playing God, then appeared in TNG: Journey's End, then again on DS9 in The Maquis, Part One, then again on TNG: Preemptive Strike, then again on DS9: Tribunal, then finally on VOY: Caretaker.
Jonathan Frakes also appeared on all three shows. Actually, he appeared on four - TNG, DS9, VOY, and ENT. He played William Riker in every episode of TNG, VOY: Death Wish, and ENT: These Are The Voyages (God, it pains me to write the title of that abomination). However, in his appearance on DS9: Defiant, he played Thomas Riker. So the same character didn't appear in each 24th century show, so he doesn't count.

Marina Sirtis also appeared as the same character, Deanna Troi, on three of the shows - TNG, VOY, and ENT. However, she never appeared on DS9 as any character, so she doesn't count either.

Looks like you just got stumped!

