Abstract: Superconducting quantum interference device (SQUID) is one of the most sensitive magnetic flux sensors and has been widely used in geomagnetic and biomagnetic detection, quantum metrology, and scientific instrumentation. Cryogenic current comparator (CCC) utilizes SQUIDs to measure minute current variations in conductors, enabling high-precision current ratio measurements and resistance comparisons. This paper introduces a discrete overlap-coupling SQUID with additional positive feedback (APF) designed for CCC systems. The SQUID adopts a second-order gradient structure to enhance sensitivity to small flux variations and reduce external interference. Additional positive feedback is integrated to improve the flux-to-voltage transfer coefficient, effectively alleviating the issue of excessive preamplifier noise in high-sensitivity applications. In addition, the APF coils, feedback coils, and input coils are all composed of multi-turn regular octagonal microstrip coils connected in series. These components are individually overlap-coupled with the SQUID washers to enhance the coupling coefficient between the loops and coils, effectively preventing mutual interference among these key components. Using our microfabrication platform, we fabricated three sets of discrete overlap-coupling SQUIDs with Nb/Al-AlO_x/Nb Josephson junctions on 4-inch silicon wafers. The hysteresis parameters β_C was set to 0.5, 1, and 2, respectively. For each set, we designed both SQUIDs with APF and control groups without APF. Low-temperature measurement results show that the dynamic resistance and flux-to-voltage transfer coefficient of the SQUID increase with the hysteresis parameter. For β_C=1, integration of the APF increases the SQUID flux-to-voltage transfer coefficient from 203 μV/Φ₀ to 324 μV/Φ₀. The total flux noise decreases from 2.4 μΦ₀/√Hz to 2.1 μΦ₀/√Hz and the total current white noise decreases from 6.7 pA/√Hz to 5.7 pA/√Hz. Meanwhile, the flux noise referred to the preamplifier is reduced from 1.6 μΦ₀/√Hz to 1.0 μΦ₀/√Hz. APF reduces the noise contribution of the preamplifier by enhancing the flux-to-voltage transfer coefficient. However, excessive APF gain may lead to system instability and introduce additional noise. Moreover, the resistance in the APF circuit generates Nyquist thermal noise, further affecting the overall system noise performance.