  The dark matter (DM) can consist of the primordial black holes (PBHs) in
addition to the conventional weakly interacting massive particles (WIMPs). The
Poisson fluctuations of the PBH number density produce the isocurvature
perturbations which can dominate the matter power spectrum at small scales and
enhance the early structure formation. We study how the WIMP annihilation from
those early formed structures can affect the CMB (in particular the E-mode
polarization anisotropies and $y$-type spectral distortions) and global 21cm
signals. Our studies would be of particular interest for the light (sub-GeV)
WIMP scenarios which have been less explored compared with the mixed DM
scenarios consisting of PBHs and heavy ($\gtrsim 1$ GeV) WIMPs. For instance,
for the self-annihilating DM mass $m_{\chi}=1$ MeV and the thermally averaged
annihilation cross section $\langle \sigma v \rangle \sim 10^{-30} \rm cm^3/s$,
the latest Planck CMB data requires the PBH fraction with respect to the whole
DM to be at most ${\cal O}(10^{-3})$ for the sub-solar mass PBHs and an even
tighter bound (by a factor $\sim 5$) can be obtained from the global 21-cm
measurements.
