In the field of high-precision physical field detection, measurements based on magnetic signals are crucial due to their exceptional accuracy, sensitivity, and stability. Superconducting Quantum Interference Devices (SQUIDs), with their ultra-high sensitivity, have become key in detecting minute changes in magnetic flux. However, with increasing demands for higher precision, further enhancing device performance under quantum constraints remains a significant challenge. This study improved the precision of SQUID sensors by optimizing the geometry of microscale washers using the physical response of superconducting films under micromachining technologies and quantum constraints. Our research extensively examined the effects of square, octagonal, and circular washers on the magnetic field response, shielding currents, and inductance. Experimental results showed that, compared to traditional square washers, octagonal washers significantly enhanced sensor sensitivity and efficiency by minimizing edge magnetic flux and optimizing current distribution. Notably, all observed inductance values exceeded predictions based on traditional empirical formulas, with square washers showing the highest average relative error of 80.8%, while circular and octagonal washers had errors of 65.31% and 66.43%, respectively. This breakthrough not only lays a new theoretical foundation for the design of SQUID sensors but also provides robust evidence for enhancing magnetic field detection through microscale technological innovation.