Let $G $ be a finite group and let $Gamma(G)$ be the prime graph of G. Assume $2 < q = p^{alpha} < 100$. We determine finite groups G such that $Gamma(G) = Gamma(U_3(q))$ and prove that if $q neq 3, 5, 9, 17$, then $U_3(q)$ is quasirecognizable by prime graph, i.e. if $G$ is a finite group with the same prime graph as the finite simple group $U_3(q)$, then $G$ has a unique non-Abelian composition factor isomorphic to $U_3(q)$. As a consequence of our results, we prove that the simple groups $U_{3}(8)$ and $U_{3}(11)$ are $4-$recognizable and $2-$recognizable by prime graph, respectively. In fact, the group $U_{3}(8)$ is the first example which is a $4-$recognizable by prime graph.