Non-central heavy-ion collisions at ultra-relativistic energies are unique in generating magnetic fields of significant strength in the laboratory. The short-lived magnetic field created at the early stages of this type of collision could impact the system's thermodynamic and transport properties of final state dynamics. In this work, we analyze the bulk thermodynamic observables such as energy density($\epsilon$), pressure(P), entropy density(s), as well as second-order quantity like the speed of sound ($c_{s}^{2}$) of a hadron gas in the presence of an external static magnetic field utilizing thermodynamically consistent non-extensive Tsallis statistics at zero chemical potential, $\mu = 0$. Further, such a system's magnetization(M) is also investigated. This analysis reveals an interplay of the diamagnetic and paramagnetic aspects of the system in the presence of the external magnetic field of distinct strengths for non-central heavy-ion collisions as one moves from RHIC to the LHC energies.