  There is a hope that looking into the early Universe with next-generation
telescopes, one will be able to observe the early accretion growth of
supermassive black holes (BHs) when their masses were $\sim 10^4$-$10^6
M_\odot$. According to the standard theory, the bulk of the gravitational
potential energy released by radiatively efficient accretion of matter onto a
BH in this mass range is expected to be emitted in the extreme UV-ultrasoft
X-ray bands. We demonstrate that such a 'miniquasar' at $z\sim 15$ should leave
a specific, localized imprint on the 21 cm cosmological signal. Namely, its
position on the sky will be surrounded by a region with a fairly sharp boundary
of several arcmin radius, within which the 21 cm brightness temperature quickly
grows inwards from the background value of $\sim -200$ mK to $\sim +30$ mK. The
size of this region is only weakly sensitive to the BH mass, so that the flux
density of the excess 21 cm signal is expected to take a nearly universal value
of $\sim 0.2[(1+z)/16]^{-2}$~mJy and should be detectable by the Square
Kilometer Array. We argue that an optimal strategy would be to search for such
signals from high-$z$ miniquasar candidates that can be found and localized
with a next-generation X-ray mission such as Lynx. A detection of the predicted
21 cm signal would provide a measurement of the growing BH's redshift to within
$\Delta z/(1+z)<0.01$.
