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In-storage processing technology allows applications to run on embedded processors and accelerators inside solid-state drives (SSDs) for efficient computing distribution. Especially, in pattern matching applications, in-storage computing can be processed quickly due to low data access latency, and the number of I/Os can be reduced by returning only a small amount of results to the host system after processing. Previously proposed in-storage processing is separated into three phases: command decoding, data access, and data processing. In this case, data processing is strictly isolated from data access, and the isolation constraints the utilization of storage. Merging data access and data processing among the phases can enhance the utilization of storage. To efficiently merge them, we propose two-stage in-storage processing architecture and scheduling, especially for the pattern matching application. The first stage processing during data access reduces the second stage processing latency. Also, leveraging the pattern matching results of the first stage processing, our scheduler prioritizes key requests that should return the results to the host system so that they are completed earlier than non-key requests. The proposed scheduling reduces the response time of in-storage processing requests by 52.6 % on average.INDEX TERMS in-storage processing, solid-state drives (SSDs), scheduling, pattern matching