Univalent functions represent a crucial area in complicated analysis applicable to both single and many variables. Researchers have performed a traditional analysis of this subject since at least 1907. Geometric function theory is synthesis for geometry & analysis. Various research has examined first-order differential subordination, subsequently leading to inquiries into second-order differential subordination within the unit disc. Abdulhalim and Miller [3] presented third-order differential subordination by reinterpreting essential inequalities of realvalued function inside  framework ofor complexvalued function. This research seeks to formulate fourth-order differential subordination & superordination by  application for generalized derivative operator Dγ,σs,m,k f(z) such that numerous theorems are stated and proved involving the generalized derivative operator Dγ,σs,m,k f(z) for analytic function [1] in open-unit disc A, which using generalised Srivastava-Attiya operator, generalised Al-Oboudi operator, binomial series. Based on this new operator, we derive results regarding fourth differential subordination and superordination technique for analytic functions related to operator Dγ,σs,m,k f(z) within the open unit disk A and we discuss these insights by examining relevant categories of admissible functions, some theories and colleries.