This manuscript presents a new weaker version of supra septarian axioms based on supra $\epsilon$-open sets, along with its essential features, which are called supra-$\epsilon$-$T_{j}$-space, $j=0,1,2$, in the framework of supra topological spaces (or STSs). We give comprehensive explanations of each type of them, backed up by several examples and counterexamples that highlight the significance of our original approaches. We also provide a diagram that outlines these relationships. Additionally, we present the supra $\epsilon$-symmetric property and supra difference property and study their effects on these version of supra-$\epsilon$-septarian axioms. In especial, we show that the two concepts of supra-$\epsilon$-$T_{0}$-space and supra-$\epsilon$-$T_{1}$-space are the same for any STS that fulfills supra $\epsilon$-symmetric property. Finally, we study the supra topological and supra hereditary properties for each of the previously discussed approaches. In particular, we show that the property of being a supra-$\epsilon$-$T_{j}$-space, where $j=0,1,2$, is a supra-hereditary (topological) property.

In this article, as an extension of the concepts of supra-E-T2-space, supra-E-T1-space, and supra-E-T0-space, we present the notion of supra-E completely space. Furthermore, we demonstrate that for any STS (γ; θ), the concepts of supra-E-T2-space and supra-E- completely-space are the same if γ less than or equal 4. We also explore the behavior of this notion with respect to specific forms of supra functions. We demonstrate that, under a bijective supra E-open function, the image of any supra-E- completely -space is a supra-E- completely. Additionally, we demonstrate that every supra subspace of supra-E- completely -space is supra-E-completely. Moreover, four new versions of separation axioms that utilize supra E-open sets are introduced namely: supra-E -regular-space, supra-E-normal-space, supra-E-T3-space, and supra-E-T4-space. We also give a general illustration of their key traits and look at the prerequisites for a number of similar links between them. We also propose a figure 1 graphic that shows these linkages. Furthermore, we demonstrate that every supra-E-R-space (γ; θ) is supra-E-N-space if γ less than or equal 4. This implies that the approaches of supra-E-T3-space and supra-E-T4-space are the same in this case. The necessary counterexamples that validate our findings are finally presented