The notion of a neutrosophic set is generally referred to as the generalization of an intuitionistic fuzzy set. Studying open and closed set variations is crucial in Neutrosophic topology, given the growing significance of Neutrosophic sets in various applications. The origin, nature, and scope of neutrality are explored through the Neutrosophic set. This concept is crucial for research due to its potential applications across various scientific and technological fields. Because the universe inherently contains indeterminacy, the Neutrosophic set provides a valuable framework for study. It is currently being developed to represent data that is uncertain, imprecise, incomplete, or inconsistent. A Neutrosophic set is described using three membership functions: truth, indeterminacy, and falsity. This approach helps to manage uncertainty and leads to more logical outcomes in practical scenarios. Additionally, the Neutrosophic set can identify inconsistencies within data and offer solutions to real-world problems. Neutrosophic functions, based on the Neutrosophic Set Theory, have broad and growing applications due to their ability to model uncertainty, indeterminacy, and inconsistency in data. Here are some of the key areas where neutrosophic functions are applied: Artificial Intelligence & Machine Learning, Data Science and Information Fusion, Decision-Making and Multi-Criteria Decision Analysis (MCDA), Business and Economics, Healthcare and Medical Diagnosis, and Control Systems and Robotics. In 2024, Suthi Keerthana Kumar, Vigneshwaran Mandarasalam, Saied Jafari, and Vidyarani Lakshmanadas described the concepts of Neutrosophic αb*ɡα-closed sets, Neutrosophic αb*ɡα-open sets, Neutrosophic αb*ɡα-border, and Neutrosophic αb*ɡα-frontier and discussed their properties in Neutrosophic topological spaces. In this research paper, we introduce the concepts of Neutrosophic αb*ɡα-continuous (Nαb*ɡα-continuous) maps, Nαb*ɡα-irresolute maps, Nαb*ɡα-closed maps, Nαb*ɡα-open maps, strongly Nαb*ɡα-continuous maps, perfectly Nαb*ɡα-continuous maps, contra Nαb*ɡα-continuous maps, and contra Nαb*ɡα-irresolute maps in Neutrosophic topological spaces. We investigate and obtain several properties and characterizations concerning these mappings in Neutrosophic topological spaces