  In this paper, a quantitative investigation of the non-classical and quantum
non-Gaussian characters of the photon-subtracted displaced Fock state
$|{\psi}\rangle=a^kD(\alpha)|{n}\rangle$, where $k$ is number of photons
subtracted, $n$ is Fock parameter, is performed by using a collection of
measures like Wigner logarithmic negativity, linear entropy potential, skew
information based measure, and relative entropy of quantum non-Gaussianity. It
is noticed that the number of photons subtracted ($k$) changes the
nonclassicality and quantum non-Gaussianity in a significant amount in the
regime of small values of the displacement parameter whereas Fock parameter
($n$) presents a notable change in the large regime of the displacement
parameter. In this respect, the role of the Fock parameter is found to be
stronger as compared to the photon subtraction number. Finally, the Wigner
function dynamics considering the effects of photon loss channel is used to
show that the Wigner negativity can only be exposed by highly efficient
detectors.
