The exploration of potassium metal batteries (PMBs) has been intensified, leveraging potassium's abundant availability, low redox potential, and small Stokes radius. Covalent triazine frameworks (CTFs) stand out for their accessible nitrogen sites and customizable structures, making them attractive electrode materials. Nonetheless, there is a lack of established design principles to guide the development of high-performance PMBs using CTFs. In this work, CTFs consisting of different monomers are used as PMB cathodes to investigate the structure-performance correlation. The electronic structure analysis reveals the polar characteristic of a CTF derived from the tetracyanoquinodimethane monomer, setting it apart with superior capacity (161 mAhg-1 at 0.1A g-1), rate performance (85 mAhg-1 at 5 Ag-1), and stability (capacity retention of 81% after 1000 cycles) over three non-polar counterparts in PMBs. Calculations based on density functional theory support the exceptional performance with increased K+ adsorption energy. Ultimately, among multifaceted factors, the polarity of CTF is the leading element that determines the K+ storage capability. These findings pave the way for the development of prudent CTF electrodes for high-performance PMBs.