<p>Fog Computing aims to offload tasks to reduce the burden on devices, enhancing efficiency and lowering latency. However, in enterprise environments, maintaining stringent control over tasks is essential, particularly for sensitive operations. User mobility and dynamic workloads introduce challenges in service migration, necessitating robust strategies for consistent service quality. Tasks with strict control requirements must be deployed within local or Fog resources within the enterprise, complicating resource allocation. Maximizing the satisfaction of these sensitivity constraints is crucial for effective system management. This study focuses on optimizing workflow partial offloading and migration in a hybrid Fog and Cloud environment, specifically targeting sensitive tasks. The primary goal is to minimize delay and energy consumption while ensuring that sensitive tasks are executed within the organization’s local and Fog resources. To achieve this, we propose a Deep Q-Network-based solution to determine the optimal policy for task offloading and migration in heterogeneous Fog-Cloud environments. By incorporating a heuristic for machine selection, our approach not only enhances Quality of Service (QoS) but also ensures strict adherence to sensitivity constraints associated to enterprise tasks. Simulations demonstrate its superior performance in reducing delay and improving energy efficiency compared to benchmark strategies.</p>