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The past decade has witnessed the rapid development of real-time wireless technologies and their wide adoption in various industrial Internet-of-Things (IIoT) applications. Among those wireless technologies, 6TiSCH is a promising candidate as the de facto standard due to its nice feature of gluing a real-time link-layer standard (802.15.4e, for offering deterministic communication performance) together with an IP-enabled upper-layer stack (for seamlessly supporting Internet services). 6TiSCH's built-in random slot selection scheduling algorithm, however, often leads to large and unbounded transmission latency, thus can hardly meet the real-time requirements of IIoT applications. This paper proposes an adaptive partition based scheduling framework, APaS, for 6TiSCH networks. APaS introduces the concept of resource partitioning into 6TiSCH network management. Instead of allocating network resources to individual devices, APaS partitions and assigns network resources to different groups of devices based on their layers in the network so as to guarantee that the transmission latency of any end-toend flow is within one slotframe length. APaS also employs a novel online partition adjustment method to further improve its adaptability to dynamic network topology changes. The effectiveness of APaS is validated through both simulation and testbed experiments on a 122-node multi-hop 6TiSCH network.