In recent years, various geometric domains have been employed to define subclasses of analytic functions aimed at deriving sharp estimates for the Taylor--Maclaurin coefficients. In this paper, we introduce and investigate a novel subclass of analytic functions associated with the four-leaf domain, which is symmetric about the real axis. For this class, we determine sharp coefficient estimates, establish Fekete--Szeg\"o inequalities and present generalized Zalcman-type functionals, along with estimates of Hankel determinants of prescribed order. Furthermore, we derive results for inverse functions and logarithmic coefficients. As an application, we introduce a generalized Hadamard product subclass and apply the derived results to generating functions associated with the Poisson, Pascal and Borel distributions. Connections to previously established results are also discussed.
Tejas et al. (Tue,) studied this question.