We continue to investigate the generalizations of the notion of wQN-space introduced by [L. Bukovský-J. Šupina: Modifications of sequence selection principles, Topology Appl. 160 (2013), 2356-2370] and by [J. Šupina: On Ohta-Sakai’s properties of a topological space (to appear)]. We present covering characterizations, slightly different formulations, and some new relations among them