Urban transportation networks are vital for the economic and environmental well-being of cities and they are faced with the integration of Human-Driven Vehicles (HVs) and Connected and Autonomous Vehicles (CAVs) challenge. Most of the traditional traffic management systems fail to effectively manage the dynamic and complex flows of mixed traffic, mainly because of large computational requirements and the restrictions that control models of traffic lights directly based on extensive and continuous training data. Most of the times, the operational flexibility of CAVs is severely compromised for the safety of HVs, or CAVs are given high priority without taking into account the efficiency of HVs leading to lower performance, especially at low CAV penetration rates. On the other hand, the existing adaptive traffic light approaches were usually partial and could not adapt to the real-time behaviors of the traffic system. Some systems operate with inflexible temporal control plans that cannot react to variations in traffic flow or use adaptive control strategies that are based on a limited set of static traffic conditions. This paper presents a novel traffic light control approach utilizing the BIRCH (Balanced Iterative Reducing and Clustering using Hierarchies) clustering algorithm combined with digital twins for a more adaptive and efficient system. The BIRCH is effective in processing large datasets because it clusters data points incrementally and dynamically into a small set of representatives. The suggested method does not only enable better simulation and prediction of traffic patterns but also makes possible the real-time adaptive control of traffic signals at signalized intersections. It also improves traffic flow, reduces congestion, and minimizes vehicle idling time by adjusting the green and red light durations dynamically based on both real-time and historical traffic data. This approach is assessed under different traffic intensities, which include low, moderate, and high, while efficiency, fuel consumption, and the number of stops are being compared with the traditional and the existing adaptive traffic management systems.