  The observed spectral energy distribution of an accreting supermassive black
hole typically forms a power-law spectrum in the Near Infrared (NIR) and
optical wavelengths, that may be interpreted as a signature of accelerated
electrons along the jet. However, the details of acceleration remain uncertain.
In this paper, we study the radiative properties of jets produced in
axisymmetric GRMHD simulations of hot accretion flows onto underluminous
supermassive black holes both numerically and semi-analytically, with the aim
of investigating the differences between models with and without accelerated
electrons inside the jet. We assume that electrons are accelerated in the jet
regions of our GRMHD simulation. To model them, we modify the electrons'
distribution function in the jet regions from a purely relativistic thermal
distribution to a combination of a relativistic thermal distribution and the
$\kappa$-distribution function. Inside the disk, we assume a thermal
distribution for the electrons. We calculate jet spectra and synchrotron maps
by using the ray tracing code {\tt RAPTOR}, and compare the synthetic
observations to observations of Sgr~A*. Finally, we compare numerical models of
jets to semi-analytical ones. We find that in the $\kappa$-jet models, the
radio-emitting region size, radio flux, and spectral index in NIR/optical bands
increase for decreasing values of the $\kappa$ parameter, which corresponds to
a larger amount of accelerated electrons. The model with $\kappa = 3.5$,
$\eta_{\rm acc}=5-10\%$ (the percentage of electrons that are accelerated), and
observing angle $i = 30^{\rm o}$ fits the observed Sgr~A* emission in the
flaring state from the radio to the NIR/optical regimes, while $\kappa = 3.5$,
$\eta_{\rm acc}< 1\%$, and observing angle $i = 30^{\rm o}$ fit the upper
limits in quiescence.
