Searchable encryption (SE) enables searching encrypted data for useful information without full decryption. Asymmetric searchable encryption (ASE) allows anyone to encrypt data \(\textbf{y}\) with a public key, producing ciphertext \(\textsf{ct}_\textbf{y}\) . Given a predicate \(P_\textbf{x}(\cdot )\) over an attribute \(\textbf{x}\) , a testing token \(\textsf{Tk}_\textbf{x}\) can be generated to evaluate \(P_\textbf{x}(\textbf{y})\) from \(\textsf{ct}_\textbf{y}\) . It is crucial to ensure that the token holder cannot infer information about \(\textbf{x}\) from \(\textsf{Tk}_\textbf{x}\) , even after evaluating the predicate on multiple ciphertexts. An ASE system meeting this requirement is called an enhanced predicate-private ASE. This paper proposes an enhanced predicate-private ASE system for conjunction predicates, based on standard lattice-based hard problems. This is the first post-quantum enhanced predicate-private ASE system supporting predicates beyond equality. At its core is a predicate-private Hidden Vector Encryption (HVE) scheme that handles large attribute universes. Our system enables privacy-preserving pattern matching on encrypted data, making it practical for various secure applications.