Reconfigurable Intelligent Surfaces (RIS) is becoming a transformative technology for the upcoming 6G communication networks, providing a way for smartly maneuvering the electromagnetic waves to enhance coverage and connectivity. This paper presents an efficient handover (HO) management scheme leveraging RIS in the Fresnel region i.e., in both the near-field (NF) and far-field (FF) regions to reduce signaling overhead and optimize mobility management. For this, we analyzed the signal strength variations in the considered RIS-aided networks, considering the radiative NF and FF regions, and derive the probability density function (PDF) of the RIS-UE distance in the NF region to quantify RIS reflection gains along the user equipment (UE) trajectory. We propose a new HO algorithm incorporating several HO categories like hard handover (HHO), soft handover (SHO), RIS-aided cell breathing (RIS-CB), and RIS-aided ping-pong avoidance (RIS-PP) strategies. The proposed algorithm uses bit error rate (BER) as a key parameter to predict the minimization of unnecessary HOs by using RIS-aided pathways to retain connectivity with the serving base station (BS), which minimizes the requirement for frequent target BS searching and ultimately optimizes the HO. By restricting measurement reports and HO requests, the suggested method improves spectrum efficiency (SE) and energy efficiency (EE), especially in crowded cellular networks. Numerical results highlight significant reductions in HO rates and signaling load, ensuring seamless connectivity and improved quality of service (QoS) in 6G systems.