The storage ring of the high energy photon source will be driven by five 166.6 MHz β = 1 quarter-wave superconducting cavities operating at 4 K. A higher-order-mode-damped superconducting cavity was designed with excellent rf and mechanical properties based on the successful development of the proof-of-principle cavity. The mechanical design of the dressed cavity was focused on addressing stress safety throughout the processes, tunability, frequency detuning due to pressure fluctuation, and Lorentz force, among other factors. A new liquid helium vessel was designed along with a comprehensive stiffening scheme to mitigate the surging peak stress on the cavity resulting from the significantly unequal beam pipe size. In the first batch, three cavities were manufactured, and surface preparations were carefully conducted to eliminate defects and etching traces while ensuring cleanliness. The cavity’s Q0 at the design voltage of 1.5 MV reached 3.8 × 109 at 4 K, comfortably surpassing the design goal. Field emission onset was not observed during the entire test up to a peak electric field of 60 MV/m, thanks to the optimized processing procedures. Subsequently, one cavity was welded with the newly designed helium vessel and vertically tested at 2 K, achieving an rf performance comparable to the bare cavities, demonstrating the success of the jacketed cavity. This paper presents the design, fabrication, surface preparation, and cryogenic tests of the first higher-order-mode-damped 166.6 MHz β = 1 superconducting cavity.