Due to limited computing and storage resources, light clients and full nodes coexist in a typical blockchain system. Any query from light clients must be forwarded to full nodes for execution, and light clients verify the integrity of query results returned. Since existing verifiable queries based on an authenticated data structure (ADS) suffer from significant network, storage and computing overheads by virtue of verification objects (VOs), an alternative way turns to the trusted execution environment (TEE), with which light clients do not need to receive or verify any VO. However, state-of-the-art TEEs cannot deal with large-scale applications conveniently due to the limited secure memory space (e.g., the size of the enclave in Intel SGX (software guard extensions), a typical TEE product, is only 128 MB). Hence, we organize data hierarchically in trusted (enclave) and untrusted memory, along with hot data buffered in the enclave to reduce page swapping overhead between two kinds of memory. The cost analysis and empirical study validate the effectiveness of our proposed scheme. The VO size of our scheme is reduced by one to two orders of magnitude compared with that of the traditional scheme.