  Fallback in core-collapse supernovae (CCSNe) plays an important role in
determining the properties of the central compact remnants, which might produce
a black hole (BH) hyperaccretion system in the centre of a massive CCSN. When
the accretion rate is extremely high and neutrino cooling is dominant, the
hyperaccretion should be in the phase of the neutrino-dominated accretion flows
(NDAFs), and thus a large number of anisotropic MeV neutrinos will be launched
from the disc along with the strong gravitational waves (GWs). In this paper,
we perform a series of one-dimensional CCSN simulations with the initial
explosion energy in the range of $2-8$ B (1 B = $10^{51}$ erg) to investigate
the fallback processes. By considering the evolution of the central BH mass and
spin in the fallback accretion, we present the effects of the initial explosion
energies, masses and metallicities of the massive progenitor stars on the
spectra of anisotropic MeV neutrinos and the waveform of GWs from NDAFs. These
neutrino or GW signals might be detected by operational or future detectors,
and the multimessenger joint detections could constrain the properties of CCSNe
and progenitor stars.
