Are there new fundamental particles and interactions Beyond the Standard Model of particle physics (BSM)? The most fascinating open questions in our current understanding of Nature support a positive answer. For example, the dark matter in our universe could be explained by new fundamental particles weakly coupled to the SM. Similarly, the unexplained Charge-Parity symmetry violation in strong interactions can be solved by introducing a new light particle, the axion. Some recent, intriguing anomalies in cosmic radiation have thrilled the community as potential evidence for new physics BSM. My project will shed new light on them by exploiting forthcoming observations of the very high energy sky with innovative techniques. A long-standing excess of gamma-rays at GeV energies is measured towards the Galactic Center (GCE), and could be the very first signature of particle dark matter in our Galaxy. Cosmic ray accelerators could also explain the signal, but numerous modeling uncertainties prevent to firmly assess their contribution to the excess. I will use gamma rays at TeV energies to robustly characterise the TeV halos of cosmic ray accelerators and their contribution to the GCE, thus closing on the dark matter properties compatible with it. Besides, these sources will serve as an unique laboratory to constrain cosmic ray acceleration and propagation in the interstellar medium. This work will be instrumental to deeply investigate a new, promising signatures of photon-axion interactions, that is the modulation of the gamma-ray spectrum of Galactic cosmic ray accelerators. By exploiting the unprecedented energy resolution of forthcoming gamma-ray data at very high energy, I will search for axion-like-particle signatures in a yet unexplored parameter space. At LAPTh I will have access to the crucial expertise needed to successfully carry out the designed project, which will strategically complement my current research profile to flourish as a senior researcher.