  We construct a generalized version of the photon-subtracted squeezed vacuum
states (PSSVS), which can be utilized to construct the same for nonlinear,
deformed and any usual quantum mechanical models beyond the harmonic
oscillator. We apply our general framework to trigonometric P\"oschl-Teller
potential and show that our method works accurately and produces a proper
nonclassical state. We analyze the nonclassicality of the state using three
different approaches, namely, quadrature squeezing, photon number squeezing and
Wigner function and indicate how the standard definitions of those three
techniques can be generalized and utilized to examine the nonclassicality of
any generalized quantum optical states including the PSSVS. We observe that the
generalized PSSVS are always more nonclassical than those arising from the
harmonic oscillator. Moreover, within some quantification schemes, we find that
the nonclassicality of the PSSVS increases almost proportionally with the
number of photons subtracted from the generalized squeezed vacuum state. Thus,
generalized PSSVS may provide an additional freedom with which one can regulate
the nonclassicality and obtain an appropriate nonclassical state as per
requirement.
