Due to the large-scale data streams produced by distributed terminals, hybrid-storage blockchain (HSB) that combines on-chain and off-chain storages has emerged as a promising solution for secure data storage in decentralized applications. Because all the raw data is outsourced to an untrusted service provider (SP), existing solutions suggest to utilize an on-chain authenticated data structure (ADS) to verify query results retrieved off-chain. However, existing solutions support onlycoarse-grained authenticationmaking a user abandon all the query results once the validation fails. In this paper, we focus on realizingfine-grained authenticationfor range queries, enabling a user to distinguish authentic data from falsified results. Considering the heavy gas consumption of on-chain storage, we propose two multi-dimensional parity-based verification (MPV) schemes with a trade-off between off-chain and on-chain efficiencies. Our main idea is to design an accumulator-based ADS to summarize well-designed verifiable hypercubes, so that fake results can be quickly located by combining multi-dimensional faces failed validation. Compared with previous solutions, our MPV schemes allow a user to make efficient use of query results by filtering out errors, and thus have higher data utility. The detailed security analysis and extensive experiments demonstrate the security and effectiveness of our MPV schemes, respectively.