In recent years, the unprecedented experimental control of the laws of quantum mechanics has led to the so-called quantum technology revolution, a terminology adopted to refer to the applications in which quantum properties play a prominent role. Also the fundamental physics has benefited from these advancements with the development of quantum simulators, controlled quantum platforms engineered in such a way to emulate the physics of complex systems difficult to investigate with classical approaches. The present work deals with the simulation of some fundamental properties of quantum-Hall systems by means of degenerate fermionic Ytterbium atoms confined in artificial periodic potentials. Extreme regimes, inaccessible to real solid-state system, have been explored, paving the way to the observation of exotic phases of matter.