We derive the Fock and position-space representations of squeezed vacuum states and their photon-added extensions associated with the para-Bose oscillator algebra of order \(\mathcal{P}=2\lambda +1\) , which constitutes a parity deformation of the standard harmonic oscillator algebra recovered at \(\mathcal{P}=1\) . For orders greater than one, we establish the resolution of the identity for both squeezed vacuum states and arbitrary m-photon-added squeezed vacuum states over the unit disk by constructing appropriate positive-definite measures, which depend on \(\lambda \) and on the pair \((\lambda ,m)\) , respectively. For odd values of the deformation order, we obtain the Wigner function of the squeezed vacuum states in phase space in the position representation and show that the emergence of negative regions, absent in the harmonic oscillator case, serves as a clear signature of nonclassicality for \(\mathcal{P}>1\) . We further analyze the individual roles of the parameters \(\lambda \) and m in enhancing or suppressing nonclassical features, including quadrature squeezing, sub-Poissonian photon statistics, photon antibunching, and entanglement in their corresponding quasi-Bell states. Optical tomograms of the m-photon–added squeezed vacuum states are constructed for even values of \(\lambda \) by solving a real eigenvalue equation for the annihilation operator. Finally, a schematic analysis is presented to elucidate how the parameters \(\lambda \) and m govern the structure of the resulting optical tomograms.
