  A hairy black hole (HBH) emerges due to matter surrounding the Schwarzschild
metric when using the Extended Gravitational Decoupling (GD) approach. The
fermionic greybody factors (GFs) and quasinormal modes (QNMs) as well as
Hawking spectra and sparsity of HBH solutions are investigated. We consider
massive and massless spin- 1/2 fermions, along with massless spin- 3/2
fermions. The equations of the effective potential for fermions with different
spins are derived in HBH spacetime. Then, the rigorous bound method is used to
calculate the fermionic spin- 1/2 and spin- 3/2 GFs. With the time domain
integration method at our disposal, we illustrate the impact of additional
parameters on the ringdown waveform of the massless fermionic spin -1/2 and
spin -3/2 fields and, in turn, on their quasinormal modes. We then delve into
investigating the Hawking spectra and sparsity of the radiation emitted by an
HBH. Hairy parameters significantly affect the sparsity of Hawking radiation as
well. We observe that the total power emitted by the BH increases both with
$\alpha$ and $Q$ but decreases with $l_{0}$. Our study conclusively shows the
significant impact of the additional parameters on important astrophysical
phenomena such as quasinormal modes, Hawking spectra, and sparsity.
