Extending Recent Congruence Results on $t$-Schur overpartitions

Recently, Nadji and Ahmia~\cite{nadji2021} introduced the notion of $t$-Schur overpartitions and investigated their combinatorial and arithmetic properties. In this paper, we extend their work and establish several new congruence relations for $t$-Schur overpartitions. For example, for all $n\ge 0$ we prove $$\overline{S_9}(24n+23)\equiv 0(\mathrm{m}\mathrm{o}\mathrm{d}32)\mathrm{.}$$