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Abstract Within the framework of residual symmetry, two ℤ 2 type associate μτ inter- change symmetries robustly constrain the Dirac CP phase δ in a model independent way. Both of them predict simultaneous maximality of δ and the atmospheric mixing angle θ 23. We show how these well known correlations will be changed if we generalize the μτ in- terchange symmetry to a μτ mixing symmetry. In particular, we show that the stringent condition of simultaneous maximality could be relaxed even with a very small departure from the exact μτ interchange. In addition, the present neutrino data on δ and θ 23 can be explained better by the mixing symmetry. After discussing the impact of the μτ mix- ing in some realistic neutrino mass models, we show how the proposed mixing could be realized with two simultaneous CP transformations which also lead to novel and testable correlations between δ and the mixing angles θij . Next we discuss in particular, the ‘three flavour regime’ of leptogenesis within the CP extended framework and show, unlike the ordinary CP extended μτ interchange symmetry, a resonant leptogenesis is possible due the generalization of μτ interchange to the μτ mixing and the resulting baryon asymmetry always requires a nonmaximal θ 23 owing to the fact that the baryon to photon ratio ηB vanishes in the exact limit of θ 23 = π/4. This is one of the robust predictions of this frame- work. The CP extended μτ mixing is also a novel example of a low energy effective model that provides an important insight to the off-diagonal terms of the flavour coupling matrix which have usually been neglected in literature to compute the final baryon asymmetry, in particular in the models with flavour symmetries.