This paper presents a novel overview in intelligent multi-access QoS mobile edge computing (MEC) for beyond 5G networks and services. There are many challenges faced by the expansion of Cloud networks and Mobile networks, which can be solved by providing connectivity at the edge of the network, i.e. with Mobile Edge Computing networks. The MEC improves overall network performance and reduces end-to-end service delay. Also, the improved advanced QoS model including Machine Learning (ML) algorithm within for next generation of mobile networks and services are proposed. The purpose of the ML algorithm is to understand the traffic activity and determine how the traffic schedule should be made. Given a set of machines and a set of jobs, the model should compute the processing schedule that minimizes specified metrics. The proposed model combines the most powerful features of both Cloud and Edge computing, independent from any existing and future Radio Access Technology, leading to possible better performance utility networks, lower service delay with high QoS provisioning for many used multimedia service. Finally, this paper gives an overview of the existing Mobile Edge Computing technologies and several existing use cases. Undoubtedly, MEC with QoS support is an innovative network paradigm going in 6G, which can essentially answer many of the existing Mobile Networks' challenges.