We perform a global analysis of neutrino data in the framework of three massive neutrinos with non-standard neutrino interactions which affect their evolution in the matter background. We focus on the effect of NSI in the present observables sensitive to leptonic CP violation and to the mass ordering. We consider complex neutral current neutrino interactions with quarks whose lepton-flavor structure is independent of the quark type. We quantify the status of the "hints" for CP violation, the

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... s-ordering and non-maximality of θ 23 in these scenarios. We also present a parametrization-invariant formalism for leptonic CP violation in presence of a generalized matter potential induced by NSI.