In this paper, we introduce generalised quasi-ideals in ordered ternary semigroups. Also, we define ordered m-right ideals, ordered (p, q)-lateral ideals and ordered n-left ideals in ordered ternary semigroups and studied the relation between them. Some intersection properties of ordered (m, (p, q), n)-quasi ideals are examined. We also characterize these notions in terms of minimal ordered (m, (p, q), n)-quasi-ideals in ordered ternary semigroups. Moreover, m-right simple, (p, q)-lateral simple, n-left simple, and (m, (p, q), n)-quasi simple ordered ternary semigroups are defined and some properties of them are studied.

Keywords: quasi ideal, ordered ternary semigroup