  We present the study of the quark sector of the universal seesaw model with
$\mathrm{SU(2)_L \times SU(2)_R \times U(1)_{Y'}}$ gauge symmetry in the
massless case of the two lightest quark families. This model aims to explain
the mass hierarchy of the third family quark by introducing a vector-like quark
(VLQ) partner for each quark. In this model, we introduce $\mathrm{SU(2)_L}$
and $\mathrm{SU(2)_R}$ Higgs doublets. We derive explicitly the Lagrangian for
the quark sector, Higgs sector, and kinetic terms of the gauge fields, starting
from the Lagrangian, which is invariant under $\mathrm{SU(2)_L \times SU(2)_R
\times U(1)_{Y'}}$ gauge symmetry. At each stage of the symmetry breaking, we
present the Lagrangian with the remaining gauge symmetry. Additionally, we
investigate the flavor-changing neutral currents (FCNC) of Higgs ($h$) and
$Z$-boson in the interaction with the top, heavy top, bottom, and heavy bottom
quark.
