The efficiency improvement of healthcare systems is a major national goal across the world. However, delivering scalable and reliable healthcare services to people, while managing costs, is a challenging problem. The most promising methods to address this issue are based on smart healthcare (s‐health) technologies. Furthermore, the combination of edge computing and s‐health can yield additional benefits in terms of delay, bandwidth, power consumption, security, and privacy. However, the strategic placement of edge‐servers is crucial to achieve further cost and latency benefits. This article is divided into two parts: an AI‐based priority mechanism to identify urgent cases, aimed at improving quality of service and quality of experience is proposed. Then, an optimal edge‐servers placement (OESP) algorithm to obtain a cost‐efficient architecture with lower delay and complete coverage is presented. The results demonstrate that the proposed priority mechanism algorithms can reduce the latency for patients depending on their number and level of urgency, prioritising those with the greatest need. In addition, the OESP algorithm successfully selects the best sites to deploy edge‐servers to achieve a cost‐efficient system, with an improvement of more than 80%. In sum, the article introduces an improved healthcare system with commendable performance, enhanced cost‐effectiveness, and lower latency.