This paper addresses the integration of epistemic entrenchment into paraconsistent belief revision systems based on Logics of Formal Inconsistency (LFIs). While systems like AGMp and AGMo adapt AGM principles to paraconsistency, they lack mechanisms to rank beliefs, primarily due to the absence of properties such as the replacement property in the underlying logics. We introduce two novel logics, Cbr and RCBr, with the latter extending the former to fully address these limitations given that it is self-extensional. Using RCBr, we define contraction operations via epistemic entrenchment, adhering to key rationality principles. Our framework leverages non-deterministic matrix semantics (Nmatrices) and Boolean algebras with LFI operators (BALFIs), providing a robust foundation for paraconsistent reasoning. These contributions advance the theory of paraconsistent belief revision and pave the way for applications in domains such as multi-agent systems and inconsistent knowledge bases.

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