been recently shown that the flavored-mass terms can also be constructed for staggered fermions [@KS; @Suss; @Sha] in Ref. [@Adams1; @Adams2; @Hoel]. The original purpose of introducing these terms was establishment of the index theorem with staggered fermions [@Adams1]. A bonus here is that staggered fermions with the flavored-mass terms can be applied to lattice QCD simulations as Wilson fermion and an overlap kernel. One possible advantage of these novel formulations, called staggered-Wilson and staggered-overlap, is reduction of matrix sizes in the Dirac operators, which would lead to reduction of numerical costs in lattice simulations. The numerical advantage in the staggered-overlap fermion have been shown in [@PdF]. Now further study is required toward lattice QCD with these lattice fermions.

The purpose of this work is to reveal properties of staggered-Wilson fermions in terms of the parity-phase structure (Aoki phase) [@AokiP; @AokiU1; @CreutzW; @SS; @ACV; @Sharpe]. As is well-known, the existence of the Aoki phase and the second-order phase boundary in Wilson-type fermions enables us to perform lattice QCD simulations by taking a chiral limit since the critical behavior near the phase boundary reproduces massless pions and the PCAC relation. Besides, understanding the phase structure also gives practical information for the 