In the field of information security, protection of password storage and digital signatures is an utmost importance. The reliability of digital signatures depends heavily on the cryptographic power of primary hash functions. Beyond digital signatures, hash functions play pivotal roles in diverse cryptographic applications such as ensuring data integrity, facilitating group signatures, enabling e-cash systems, and enhancing overall security and efficiency of protocols. This research paper proposes a novel approach for storing password by applying integrated SHA-256 with Argon2id, and an advanced memory-hard functions. Through iterative hashing, salting, and the key stretching techniques, the algorithm not only enhances the security but also mitigates risks associated with traditional hashing methods has concluded with key observations in this paper.