Blockchain is a promising emerging technology that is envisioned to play a key role in establishing secure and reliable Internet-of-Things (IoT) ecosystems without the involvement of any third party. Hyperledger Fabric, a permissioned blockchain system that can yield high throughput and low consensus delay, has shown its capability in enhancing security and privacy protection for delay-sensitive IoT services. The literature, however, has not considered the conflicting transaction problem which may substantially limit the system performance and degrade QoS for the end users. In this article, we propose CATP-Fabric, a new blockchain system to address the conflicting transaction problem by reducing the number of potentially conflicting transactions with less overhead. First, the transactions within a block are divided into different groups to facilitate parallel transaction processing. Then, CATP-Fabric filters stale transactions and prioritizes the read-only transactions in each group to eliminate unnecessary overhead. Finally, we formulate the selection of aborting transactions in CATP-Fabric as a binary integer-programming problem and develop a low-complexity optimization algorithm to minimize the number of aborted transactions. Illustrative results show that our proposed CATP-Fabric blockchain system achieves high throughput of successful transactions while maintaining a lower aborting transaction rate compared to the benchmark blockchain systems.