We aimed to analyze a new class of sequential fractional differential inclusions that involves a combination of $\varsigma$-Hilfer and $\varsigma$-Caputo fractional derivative operators, along with non-separated boundary conditions. Two cases of convex-valued and non-convex-valued set-valued maps are considered. Our outcomes are obtained from some famous theorems of fixed point method within the framework of the set-valued analysis. Additionally, some examples are provided to illustrate the applicability of our outcomes.