The PADME experiment at the Beam Test Facility of the DA$\Phi$NE LINAC at INFN Laboratori Nazionali di Frascati aims to explore the existence of light, weakly interacting particles produced in positron-electron annihilation. It employs a positron beam, produced at DA$\Phi$NE LINAC, impinging on a thin target together with a detector optimised for the reconstruction of electromagnetic final states. This contribution presents the results from the Run~III data-taking campaign, where a fine scan of the center-of-mass energy was performed to probe the presence of a narrow resonance around $17~\mathrm{MeV}$, motivated by anomalies observed in nuclear transitions. No statistically significant excess is found beyond the $(1.77\pm0.15)$ standard deviations, and constraints are set on the coupling of a hypothetical vector boson to electrons, improving the sensitivity of PADME in previously unexplored regions of the parameter space. To improve the neutral background rejection capability, for the new data-taking period (Run~IV) the experiment underwent a major upgrade with the installation of a Micromegas-based tracking detector, allowing a three-dimensional track reconstruction with high spatial resolution. The detector was validated before installation and used during commissioning and data-taking, and its first performance results are reported.