[en] We proposed a scheme to generate new class of even(odd) compass states (specific superpositions of Wigner cat states [A. Dehghani et al., Ann. Phys. 362, 659 (2015)]), in the presence of the parity deformed Jaynes–Cummings Hamiltonian [A. Dehghani et al., Sci. Rep. 6, 38069 (2016)] describing a coupled system comprising a two-level atom and a cavity field assisted by a continuous external classical field. Particular attention was given to analyze their non-classical properties through of the Mandel’s parameter and quadrature squeezing. The Wigner compass states (WCSs) are compared with the ordinary ones, when the Wigner parameter becomes zero. Meanwhile generalized photon added compass states (PAWCSs) were introduced, by excitations of a newly introduced WCSs. Along with statistical analysis of latter case, a new theoretical framework for preparing them is suggested. Graphical abstract: .