This article is a continuation of generalizations in field operator theory in mathematics, such as we introduce new classes of fuzzy soft operator, which namely fuzzy soft (kˆ *– Â)-quasinormal operator in fuzzy soft Hilbert space, and shortly FS-(kˆ *– Â)-quasinormal operator. Give the text of the most important of these theorems with explains important properties for this concept and relationships with other types in the same filed finally more characterizations of FS-(kˆ *– Â)-quasinormal operator have been introduced in this article.