In this paper, we take advantage of implicit relationships to come up with a new concept called " ${\mathcal{A}}_{\vartheta }$- $\alpha$-contraction mapping". We utilized our new notion to formulate and prove some common fixed point theorems for two and four self-mappings over complete extended quasi $b$-metric spaces under a set of conditions. Our main results widen and improve many existing results in the literature. To support our research, we present some examples as applications to our main findings.