  In the current framework of Einstein's equations in general relativity (GR),
gravity is described by the spacetime curvature. However, there are other
descriptions where the origin of gravity can be understood through torsion and
non-metricity $Q$. In this work, we discuss a modified theory of gravity namely
$f(Q)$ gravity, which considers a non-linear extension of $Q$. In particular,
we study the case where it is non-minimally coupled to matter. Motivated by the
recent success of Chaplygin gas models in the explanation of dark energy, we
assume a pressureless baryonic matter and a generalized Chaplygin gas as the
background fluid. We constrain the proposed model using two different datasets:
one for Hubble measurements and the other for quasars (which we calibrated)
with Markov-Chain Monte Carlo (MCMC) methods. We employ kinematic tools such as
deceleration and jerk parameters to determine deviations of the proposed model
from $\Lambda$CDM. We establish that the transition redshift $z_T$ in the
deceleration parameter $q$ is $0.607$ and $0.204$ with the two datasets
respectively, therefore describing the universe's acceleration.
