Motivated by the morphological measures in assessing the geometrical and topological properties of a generic cosmological stochastic field, we propose an extension of the weighted morphological measures, specifically the nth conditional moments of derivative (cmd-n). This criterion assigns a distinct weight to each excursion set point based on the associated field. We apply the cmd-n on the Cosmic Microwave Background (CMB) to identify the cosmic string networks (CSs) through their unique Gott-Kaiser-Stebbins effect on the temperature anisotropies. We also formulate the perturbative expansion of cmd-n for the weak non-Gaussian regime up to O(σ30). We propose a comprehensive pipeline designed to analyze the morphological properties of string-induced CMB maps within the flat sky approximation. To evaluate the robustness of our proposed criteria, we employ string-induced high-resolution flat-sky CMB simulated patches of 7.2 deg² size with a resolution of 0.42 arcminutes. Our results demonstrate that the minimum detectable value of cosmic string tension is Gμ â‰³ 1.9 × 10^-7 when a noise-free map is analyzed with normalized cmd-n. Whereas for the ACT, CMB-S4, and Planck-like experiments at 95.45 % confidence level, the normalized cmd-n can distinguish the CSs network for Gμ ≳ 2.9 × 10^-7, Gμ ≳ 2.4 × 10^-7 and Gμ ≳ 5.8 × 10^-7, respectively. The normalized cmd-n exhibits a significantly enhanced capability in detecting CSs relative to the Minkowski Functionals.