Topological order is a fundamental concept in modern condensed matter physics, providing new paradigms for understanding strongly correlated quantum matter and offering promising applications in quantum technologies. In particular, topologically ordered phases can host anyonic excitations, including non-Abelian anyons, which are of great interest for fault-tolerant quantum computation. However, realistic quantum systems are inevitably coupled to their environments, making non-Hermitian effects an intrinsic feature of many physical platforms. Such non-Hermiticity can fundamentally alter conventional topological phenomena, giving rise to effects such as the non-Hermitian skin effect and raising important questions about the nature and stability of topological order in open systems. Recently, generalized ideal Chern bands have been proposed in the non-Hermitian Kapit–Mueller model, providing an exciting platform for exploring strongly correlated topological phases in non-Hermitian systems. Building on this development, this project aims to establish a systematic framework for studying non-Hermitian topological order and to uncover novel phases beyond those accessible in conventional Hermitian settings. We will investigate a range of exotic topological ordered states in generalized ideal Chern bands, including non-Abelian states and Halperin states, and study how their topological properties, fractionalized excitations, and robustness are modified by non-Hermiticity. Going beyond idealized models, we will further explore the realization and generalization of these topological phases in realistic open quantum systems, incorporating physically relevant dissipative processes and environmental couplings. This will allow us to bridge the gap between exactly tractable non-Hermitian models and experimentally relevant quantum platforms. Overall, the project seeks to develop a unified understanding of the interplay between non-Hermiticity, strong correlations, and topological order, opening new directions for the study of exotic quantum phases in open systems and potentially providing new routes toward robust quantum information processing.