We introduce the concept of generalized $\alpha$-$\eta $-$Z$-contraction mapping with respect to a simulation function $\zeta$ in $b$-metric spaces and study the existence of fixed points for such mappings in complete $b$-metric spaces. Further, we extend it to partially ordered complete $b$-metric spaces. We provide examples in support of our results. Our results extend the fixed point results of Olgun, Bicer and Alyildiz [Olgun, M., Bicer, O., Alyildiz, T., A new aspect to Picard operators with simulation functions. Turk. J. Math. 40 (2016), 832-837.].