In this paper, we construct integrals of motion in a para-Bose formulation for a general timedependent quadratic Hamiltonian, which, in its turn, commutes with the reflection operator. In this context, we obtain generalizations for the squeezed vacuum states (SS) and coherent states (CS) in terms of the Wigner parameter. Furthermore, we show that there is a positive completeness relation for the SS owing to the Wigner parameter. In the study of the probability transition, we found that the displacement parameter acts as a transition parameter by allowing access to odd states, while the Wigner parameter controls the dispersion of the distribution.