The J-PARC E05 experiment investigated the interaction between $\overline{K}$ and the residual nucleus via an inclusive $^{12}\rm{C}$$(K^{-}, p)$ spectrum, revealing real and imaginary $\overline{K}$ -nucleus optical potential depths of $(-80, -40)\:\rm{MeV}$. Moreover, an event excess near 100 MeV in the $\overline{K}$ binding energy suggests a bound state involving an excited hyperon $(Y^{\ast})$. A subsequent experiment, J-PARC E42, utilized the same reaction with a GEM-based HypTPC around the target. The exclusive measurement with HypTPC enhances the signal-to-noise ratio and enables the detection of the $Y^{\ast}$ nuclear state. The inclusive spectrum obtained in the E05 was reproduced also through the E42 analysis, and the analysis of particle identification and momentum measurement with HypTPC is in progress for the coming exclusive analysis.