In this paper, we have studied the magnetized quark matter (QM) and strange quark matter (SQM) distributions in the presence of f (R, T) gravity in the background of Friedmann-Lemaitre-Robertson-Walker (FLRW) metric. To get exact solutions of modified field equations we have used f (R, T) = R + 2f (T) model given by Harko et al. with two different parametrization of geometrical parameters i.e. the parametrization of the deceleration parameter q, and the scale factor a in hybrid expansion form. Also, we have obtained Einstein Static Universe (ESU) solutions for QM and SQM distributions in f (R, T) gravity and General Relativity (GR). All models in f (R, T) gravity and GR for FRW and ESU Universes with QM also SQM distributions, we get zero magnetic field. These results agree with the solutions of Aktas and Aygun in f (R, T) gravity. However, we have also discussed the physical consequences of our obtained models.