The Internet-of-Things (IoT) is an important technology and is considered the future of the Internet. Healthcare is described as one of the important areas in IoT used for remote patient monitoring. Real-time remote monitoring health applications are important as delays in data transfer between the cloud, and the application may be unacceptable. Fog computing refers to a geographically distributed computing system with several devices connected to the same network to achieve flexible and collaborative computation, storage, and communication services. Fog computing is mainly used for efficient data processing between sensors and cloud computing as it reduces the volume of data exchanged between sensors and the cloud, thereby improving the whole system's efficiency. Wireless sensor networks (WSN) are also used in health monitoring systems to simultaneously transfer huge data volumes (of different priority levels and length values) to the fog computing system. Hence, there is a need to appropriately implement a task scheduling mechanism that can accurately prioritize tasks irrespective of their length. This study aims to systematically review the existing fog computing technologies in the Internet of things HealthCare (IoTH) systems and improve the performance of the available static task scheduling algorithms using the Tasks Classification (TC) method where task importance is paramount. The performance of the suggested approach was evaluated based on the Max-Min scheduling algorithm (SA).