Federated Learning (FL) enabled edge computing has been widely used in training complex deep learning models by coordinating various heterogeneous resources in Industrial Internet of Things (IIoT). However, the existing FL solutions may cause long training time or huge energy consumption for resource-constrained terminal or edge nodes. To address this issue, we propose an adaptive edge intelligence offloading framework based on Federated Split Learning (FSL) and Reinforcement Learning (RL), named FSLEdge, for IIoT systems. To begin with, a Split Learning (SL) approach was added to FL to reduce the training time and energy consumption by allowing local devices to offload some training layers into the edge servers while ensuring the protection of private data. Additionally, FSLEdge adopts RL to find the optimal split point to adaptively identify which is the best layers of the deep learning models should be offloaded into the edge servers with the goal of reducing the training time and energy consumption. Experimental studies are conducted under two different datasets: one public, CIFAR10, and one private, GridDataset, a transmission line fault detection dataset in smart grid domain. And the results show that the training time and energy consumption of the system by our proposed FSLEdge can be reduced by 10% and 21%, respectively, compared to the classical FL, without sacrificing accuracy.