The theory of antisymmetric connectedness for a T 0-quasi-metric space was established in terms of graph theory lately, as corresponding counterpart of the connectedness for the complement of a graph. Following that in the current study, a topological localized version of the antisymmetrically connected spaces is described and studied through a variety of approaches in the context of T 0-quasi-metrics. Within the framework of this, we examine the cases under which conditions a T 0-quasi-metric space would become locally antisymmetrically connected as well as some topological characterizations of locally antisymmetrically connected T 0-quasi-metric spaces are presented, especially via metrics.