The motivation mainly comes from the conditions of (ordered) quasi-ideals to be (0-)minimal or maximal that are of importance and interest in (ordered) semigroups. In 1981, the concept and notion of a $\Gamma$-semigroup was introduced by Sen [10]. We can see that any semigroup can be reduced to a $\Gamma$-semigroup. In this article, we give some auxiliary results are also necessary for our considerations and characterize the relationship between (0-)minimal and maximal ordered quasi-ideals in ordered $\Gamma$-semigroups and $Q$-simple and 0-$Q$-simple ordered $\Gamma$-semigroups analogous to the characterizations of (0-)minimal and maximal ordered quasi-ideals in ordered semigroups considered by Iampan [5].