  We report on the discovery, structural analysis, and the physical properties
of Nb$_4$SiSb$_2$ -- a hitherto unknown compound crystallizing in the
V$_4$SiSb$_2$-type structure with the tetragonal space group $I4/mcm$ and unit
cell parameters $a$ = 10.3638(2) $\mathring{\mathrm{A}}$ and $c$ = 4.9151(2)
$\mathring{\mathrm{A}}$. We find Nb$_4$SiSb$_2$ to be a metal undergoing a
transition to a superconducting state at a critical temperature of $T_{\rm c}
\approx$ 1.6 K. The bulk nature of the superconductivity in this material is
confirmed by the observation of a well defined discontinuity in specific heat
with a normalized specific heat jump of $\Delta C(T_{\rm c})/\gamma T_{\rm c} =
1.33\, {\rm mJ}\, {\rm mol}^{-1}\, {\rm K}^{-2}$. We find that for
Nb$_4$SiSb$_2$, the unoccupied sites on the $4b$ Wyckoff position can be
partially occupied with Cu, Pd, or Pt. Low-temperature resistivity measurements
show transitions to superconductivity for all three compounds at $T_{\rm c}
\approx\, 1.2\, {\rm K}$ for Nb$_4$Cu$_{0.2}$SiSb$_2$, and $T_{\rm c} \approx\,
0.8\, {\rm K}$ for Nb$_4$Pd$_{0.2}$SiSb$_2$ as well as for
Nb$_4$Pt$_{0.14}$SiSb$_2$. The addition of electron-donor atoms into these void
positions, henceforth, lowers the superconducting transition temperature in
comparison to the parent compound.
