In this paper, we explore the connection between fixed-point and parametrized modalities in linear logic. We tackle this by examining a broad range of systems, taking inspiration from the subexponential system from Nigam and Miller and the super exponential system from Bauer and Laurent. Our work is inspired by Baillot's research on light linear logics with recursive types, but also extends to systems with multiple modalities not necessarily exponential, like Bauer and Saurin's modal calculus-based linear system. Unlike Baillot's approach, we focus on inductive and coinductive types in a non-wellfounded context, rather than finite recursive types. We introduce a new non-wellfounded system, µ-superLL, which is a variant of superLL with fixed-point, and prove a syntactic cut-elimination for it using methods from non-wellfounded linear logic.