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In this paper, we have studied the magnetized quark matter (QM) and strangequark matter (SQM) distributions in the presence of $ f(R,T)$ gravity in thebackground of Friedmann--Lema\^itre--Robertson--Walker (FLRW) metric. To getexact solutions of modified field equations we have used $f(R,T) = R + 2 f(T)$model given by Harko et al. with two different parametrization of geometricalparameters \textit{i.e.} the parametrization of the deceleration parameter $ q$, and the scale factor $ a $ in hybrid expansion form. Also, we have obtainedEinstein Static Universe (ESU) solutions for QM and SQM distributions in$f(R,T)$ gravity and General Relativity (GR). All models in $f(R,T)$ gravityand GR for FRW and ESU Universes with QM also SQM distributions, we get zeromagnetic field. These results agree with the solutions of Akta{\c{s} andAyg\"un in $f(R,T)$ gravity. However, we have also discussed the physicalconsequences of our obtained models.

FLRW cosmological models with quark and strange quark matters in f(R,T) gravity