6G Mobile Edge Computing (MEC) plays a critical role in next-generation wireless networks, requiring efficient resource management to ensure low-latency and high reliability services. Such resource management mechanisms must consider various resources including computational capabilities of mobile edge servers, available wireless bandwidth, transmission power, and Reconfigurable Intelligent Surfaces (RIS) elements that enhance signal quality and coverage. Current research demonstrates significant gaps in optimized admission control strategies for RIS-enhanced communication, limiting academic and industrial capability to fully leverage RIS technology for improved network performance. Additionally, existing resource allocation approaches often fail to address the diverse Quality of Service (QoS) requirements characteristic of 6G users, resulting in suboptimal network efficiency. The inherent complexity of 6G MEC environments, which involve multiple interdependent resources, further necessitates sophisticated joint optimization approaches. This research focuses on designing algorithms for three key aspects: admission control, resource allocation, and joint resource optimization. Critical considerations include user priority, RIS reflection constraints, and MEC computational and computing limitations. The primary objective is to develop a comprehensive optimization framework that maximizes utility while improving 6G MEC network resource management through enhanced efficiency, optimized allocation strategies, and effective joint resource optimization framework that satisfy the diverse QoS requirements of next-generation wireless users.