Graphs have been a powerful tool that is suitable for a large variety of applications including chemical databases and the Semantic Web, among others. A fundamental query of graph databases is subgraph query: given a query graph q, it retrieves the data graphs from a database that contain q. Due to the cost of managing massive data coupled with the computational hardness of subgraph query processing, outsourcing the processing to a third-party service provider is an appealing alternative. However, security properties such as data integrity and the response time are critical Quality of Service (QoS) issues in query services. Unfortunately, to our knowledge, authenticated subgraph query services have not been addressed before. To support the service, we propose Merkle IFTree (MIFTree) where Merkle hash trees are applied into our Intersection-aware Feature-subgraph Tree (IFTree). IFTree aims to minimize I/O in a well-received subgraph query paradigm namely the filtering-and-verification framework. The structures required to be introduced to verification objects (VOs) and authentication time are minimized. Subsequently, the overall response time is minimized. For optimizations, we propose an enhanced authentication method on MIFTree. Our detailed experiments on both real and synthetic datasets demonstrate that MIFTree is clearly more efficient than a baseline method.