Parity of parts and excludant statistics in partitions

In this paper, we study restricted excludant statistics depending on its parity in partitions where parts with same parity are distinct. Using $q$-series transformations, we show that generating functions of these partition statistics are related to the quantum modular forms $\text{s}(q)$, its companion ${\sigma }^{\ast }(q)$ introduced by Ramanujan, and $v_2(q)$, a Nahm-type sum, introduced by Andrews. Utilizing Tauberian method, we obtain asymptotics of such sequences.