We present the first results of the SUPAX experiment. A limit for the kinetic mixing parameter of dark photons with masses of $\sim 34 \, \mu$eV is presented. The SUPAX experiment is a RF-cavity based haloscope searching for dark matter candidates. The SUPAX experiment has been set up in 2022 at the University of Mainz. From the first measurement, intended to show the proof of concept of the experiment, a limit on the kinetic mixing parameter $\chi < (6.20 \pm 3.15^\text{(exp.)} \pm 9.65^\text{(SG)}) \cdot 10^{-14}$ at 95% CL could be set, as previously shown. The results of this paper have been showcased in the presented poster.