In this paper, a new class of sets called minimal rgw⍺-locally open sets and maximal rgw⍺-closed sets in topological spaces are introduced, which are sub classes of rgw⍺-locally open sets and rgw⍺-locally closed sets. Also we introduce and study maximal rgw⍺-locally open sets and minimal rgw⍺-locally closed sets in topological spaces and also study 𝜏_rgw⍺lc-min and 𝜏_rgw⍺lc-max spaces.