The survey of the existing literature shows that a lot of interesting fixed point problems of Banach-type have been investigated in both metric and other extended metric spaces. Nonetheless, a few of the current findings employed the recent approach of polynomial contractions. Therefore, based on the new idea of this family of contractions, this article introduces the frame of $C^{*}$ -algebra-valued partial suprametric space as an extension of suprametric spaces, and then establishes some fixed point results via the polynomial contractions. Since the proposed contractive inequality involves higher order polynomial terms, the obtained principal result can be specialized in different ways, thereby making it possible to unify, deduce, and refine several corresponding results. Contrasting illustrations are formed to indicate the preeminence of the results proposed herein. From application point of view, some of the consequences of the main finding are employed to establish new conditions for solving an anti-periodic boundary value problem for nonlinear first order differential equations of Caratheodory’s-type.
