We report on the design and implementation of AQFP buffer gates utilizing cross-type Nb/AlOx/Nb Josephson junctions with IC of 20 µA, designed to operate at mK temperatures. We, therefore, discuss design considerations, circuit simulation and optimization and their technological implementation. The preliminary results of the test circuit at 4.2 K are demonstrated focusing on the performance. Particularly, we emphasize on the current sensitivity of the circuit based on the output switching probability. The measurement results, show a narrow grayzone width of 0.48 µA for low-speed operation, demonstrating a higher current sensitivity. Additionally, the designed AQFP circuit exhibits a wide operating margins, further endorsing their potential for high sensitivity based superconducting sensors and scalable interface circuits for quantum electronics.