In this paper, we introduce the concept of neutrosophic $G$-sequential continuity as a new tool to further studies presenting the definitions of neutrosophic soft sequence, neutrosophic soft quasi-coincidence, neutrosophic soft $q$-neighborhood, neutrosophic soft cluster point, neutrosophic soft boundary point, neutrosophic soft sequential closure, neutrosophic soft group, neutrosophic soft method, which constitute a base to define the concepts of neutrosophic soft $G$-sequential closure, neutrosophic soft $G$-sequential derived set, $G$-sequentially neutrosophic soft compactness of a subset of a neutrosophic soft topological space. Their characters are analyzed and some implications are given. A counterexample to each implication is also given.

Continuity, in particular sequential continuity, is an important subject of investigation not only in Topology, but also in some other branches of Mathematics. Connor and Grosse-Erdmann remodeled its definition for real functions by replacing {\sf lim} with an arbitrary linear functional $G$ defined on a linear subspace of the vector space of all real sequences. Then, this definition was extended to a topological group $X$ by replacing a linear functional $G$ with an arbitrary additive function defined on a subgroup of the group of all $X$-valued sequences. Also, some new theorems in generalized setting were given and some other theorems that had not been obtained for real functions were presented. In this study, we introduce neutrosophic $G$-continuity and investigate its properties in neutrosophic topological spaces.