  In light of the recent result published by the Fermilab Muon $(g-2)$
experiment, we investigate a simple model that includes particles of fractional
electric charges: a colour-singlet fermion and a scalar with charges $2/3e$ and
$1/3e$, respectively. The impact of these particles on the anomalous muon's
magnetic moment is examined, particularly the restrictions on their Yukawa
couplings with the light leptons. Given that lepton flavor violation processes
impose stringent constraints on certain scenarios beyond the Standard Model, we
asses the one-loop contribution of the new particles to $(g-2)$ in order to
identify regions in the parameter space consistent with the Fermilab results
and compatible with the current and projected limits on the branching ratio
$Br(\mu \rightarrow e \gamma)$. Taking into account the current lower bound for
the masses of fractionary charged particles, which is around 634 GeV, we show
that the mass of the scalar particle with fractional charge must exceed 1 TeV.
In particular, we present some estimatives for double production of the
colour-singlet fermion at the 14 TeV LHC. Finally, we also study the validity
of our model in light of the QCD lattice results on the muon $(g-2)$.
