Only, Sole, Unique
adverb, の adjective
It's solely one. The only one. The sole one. Totally unique.
ゆいつ, ゆいいつ
The reading for 唯 is the same as the one you learned with the kanji, though there is also a shortened version which has ゆい shortened to ゆ. The reading for 一 is the one you learned with 統一, so you should be able to read it already!
あいつは奴の家族の中で唯一まともな人間だよ。
He is the only decent person in his family.