This study presents a new M*-Noor hybrid approach for approximating fixed point of Kannan Suzuki Condition (KSC) type mappings in CAT(0) space. This method combines M* iteration with the Noor iteration, using three control parameters to enhance flexibility and convergence. Theoretical analysis confirms that our method achieves both Δ-convergence and strong convergence given certain mild assumptions. Numerical results, including an application to a fractional differential equation, demonstrate that the proposed hybrid scheme achieves significantly faster and more stable convergence when evaluated against traditional M*- iteration and other well established iterative methods from existing research.