unika

Unika means one of a kind, the only one of its type in existence. It is not a synonym for "unusual", and it does not take tre or pli comfortably: a thing either is the only one or it is not. For merely unusual you want stranga or nekutima, and for remarkable, speciala.

Keep it apart from sola as well. Sola is alone, on its own, the only one present: li sidis sola. Unika is the only one that exists anywhere. La sola ekzemplero en la ĉambro and la unika ekzemplero en la mondo are different claims.

And the seam is false. You cannot build unika out of unu plus anything: Esperanto has no -ik- suffix that would do it, and unik- is a single unanalysable root. The Latin ancestors unus and unicus are of course related, so the resemblance is not pure coincidence, but that is history rather than word-building. To make an adjective from unu inside Esperanto you get unua, "first", which means something else entirely.