  In this paper we construct a black hole solution surrounded by superfluid
dark matter (BH-SFDM) and baryonic matter, and study their effects on the
shadow images of the Sgr A$^{*}$ black hole. To achieve this goal, we have
considered two density profiles for the baryonic matter described by the
spherical exponential profile and the power law profile including a special
case describing a totally dominated dark matter galaxy (TDDMG). Using the
present values for the parameters of the superfluid dark matter and baryonic
density profiles for the Sgr A$^{*}$ black hole, we find that the effects of
the superfluid dark matter and baryonic matter on the size of shadows are
almost negligible compared to the Kerr vacuum black hole. In addition, we find
that by increasing the baryonic mass the shadow size increases considerably.
This result can be linked to the matter distribution in the galaxy, namely the
baryonic matter is mostly located in the galactic center and therefore, by
increasing the baryonic matter can affect the size of black hole shadow
compared to the totally dominated dark matter galaxy where we observe an
increase of the angular diameter of the Sgr A$^{*}$ black hole of the magnitude
$10^{-5} \mu$arcsec.
