The present work introduces three new spaces: a semi-strong metacompact J-space, a semi-weak metacompact J-space, and a weak metacompact J-space. These spaces are variant of metacompact J-spaces and strong metacompact J-spaces. These spaces represent a generalization of the concepts of metacompact spaces and 𝐽-spaces introduced by E. Michael. This paper presents a generalization of J-spaces by weakening certain topological conditions to include a broader class of topological spaces. We investigate the fundamental properties of this new class and establish relationships with existing topological spaces. Several results and properties are obtained that contribute to a better understanding of J-spaces and their generalizations. In the second section of this paper, we review some definitions and theories essential to our work. Section three introduces the basic definitions of spaces semi-strong metacompact J-spaces, semi-weak metacompact J-spaces and weak metacompact J-spaces, and studies their fundamental properties, examples to illustrate some of these properties, and examines of the relationship between these spaces and metacompact J-spaces and strong metacompact J-spaces. Finally, the fourth section examines the relationship between (semi-strong metacompact J-spaces, semi-weak metacompact J-spaces and weak metacompact J-spaces) and (semi-strong J-spaces, semi-weak J-spaces and weak J-spaces), respectively, where the condition of countably compact is necessary for the equivalence of these spaces.