The concept of ideals in algebraic structures has undergone significant generalizations, especially within BCK, BCI, BCH, KU-algebra, to accommodate non-associative and non-commutative operations. While many types of PS-ideals have been studied, However, the extensive study of ideals in PS- algebra is still limited. This presents a notable gap in the literature, particularly regarding their formal characterization and existence in finite systems. This paper introduces and classifies distinct types of PS-ideals and focuses on the construction and verification of a non-trivial ideal within a finite set under a specifically defined binary operation. Through detailed analysis, we show that the subset ideal satisfies some conditions, offering a concrete example that enhances our understanding of ideal theory in generalized algebraic structures. The findings contribute to the theoretical development of PS-ideals and open new directions for further algebraic investigations, particularly in the study of minimal and non-classical algebraic systems.