With the escalating demand for portable electronic devices and electric vehicles, there is a critical need for advancements in battery performance metrics. In this context, lithium, sodium, and potassium ion batteries (LIBs, SIBs, and KIBs, respectively) with electrodes based on covalent organic frameworks hold great promise for energy storage. Herein, we applied nanostructures (COFs, COFs@CNT, and functionalized CNTs with carboxyl (-COOH), hydroxyl (-OH), and amino (-NH2) groups (F-CNT@COFs) as superior materials for energy storage applications, specifically for LIB, SIB, and KIB. Next, the effect of functionalizing with -COOH and -NH2 groups was analyzed and compared. Furthermore, the Li/Na/K-ion storage mechanism and the substrate structure's stability were studied through molecular dynamics simulation and well-tempered metadynamics. Moreover, interactions involving pi-pi stacking between layers of COFs have been proven to enhance the conductivity. Most importantly, the main point is realizing rapid Li/Na/K-ion diffusion kinetics toward the active sites of COFs, COFs@CNTs, and F-CNTs@COFs. Our findings suggest that the movement of Li+ toward the positive electrode material is notably more pronounced than other ions' migration throughout the charging and discharging processes. Moreover, the storage energy is influenced by active sites, which include contributions from C=N, C=O, and the interaction cations-pi bonds. In addition, the results of the free energy identified that the energy values for the Li+/COFs and Li+/COOH-CNT@COFs systems at their global minima are approximately similar to -512.127 kJ mol(-1) and similar to -650.86 kJ mol(-1), respectively.