Blockchain technology has revolutionized decentralized transactional data storage, fostering trustless interactions via consensus mechanisms involving miners. The security of these systems hinges on digital signatures, predominantly elliptic curve cryptography, which is at risk from quantum computing advancements. To tackle scalability and cost issues of on-chain transactions, off-chain solutions, notably payment channel networks (PCNs), have been introduced. Among these solutions, adaptor signatures (AS) have emerged as a pivotal cryptographic tool, allowing secure and efficient off-chain interactions by extending conventional signature schemes with additional hard relations tailored for payment channels. Existing post-quantum secure AS schemes, such as LAS and SQI-AS, face challenges ranging from high off-chain communication costs to security vulnerabilities. These schemes often lack consideration for the unlinkability notion of AS and may fail to deliver promised security guarantees. In response to these challenges, our contribution aims to bridge the gap in practical and secure post-quantum AS solutions. Our work introduces an isogeny-based adaptor signature utilizing the CSI-FiSh signature scheme. We define a variant, Modified CSI-FiSh (MCSI-FiSh), which incorporates a strong random self-reducible relation derived from CSIDH. Our proposed adaptor signature scheme for MCSI-FiSh not only verifies a valid signature but also ensures the release of a witness. We provide rigorous security proofs, demonstrating our scheme’s resilience against pre-signature adaptability, strong-full extractability and unlinkability. Our scheme is the first post-quantum adaptor signature offering unlinkability and strong-full extractability. We remark that the overhead of our scheme is also minimal in terms of communication cost and signature size compared to the existing post-quantum adaptor signature.