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Low-emittance photoinjector-enabled cutting-edge scientific instruments, such as free-electron lasers, inverse Compton scattering light sources, and ultrafast electron diffraction, will greatly benefit from the improved repetition rate. In this paper, we proposed a specifically designed S-band radio frequency (RF) photoinjector to obtain low emittance and kilohertz (kHz) high-repetition rates simultaneously. By lowering the gradient, much lower RF power is needed to feed the electron gun, and then the heat problem is much easier to handle. Meanwhile, by optimizing the length of the gun's first cell from the normal case of 0.6-cell to 0.4-cell, the launch phase and the extraction field are significantly improved, thus ensuring the generation of low-emittance electron beams. In our design, the proposed 1.4-cell RF gun can work effectively under different field gradients ranging from 30 MV/m to 100 MV/m. For a standard case of 60 MV/m, 2.5 MW peak RF power with ys level pulse width is sufficient, thus offering the feasibility of improving the repetition rate to kHz level with a standard 5 MW irradiation klystron. In addition, simulated electron beams with a low emittance of 0.29 mm.mrad@200 pC can be generated by this proposed photoinjector, showing that this high-repetition rate injector holds the potential to deliver high-quality beams comparable to those of state-of-the-art S-band photoinjectors. Combining the merits of low emittance and high-repetition rate, this proposed photoinjector will provide a new possibility for future free-electron laser facilities operating at repetition rates ranging from kHz to tens of kHz. [ABSTRACT FROM AUTHOR]