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We propose a non-renormalizable    $$B-L$$  B - L model with    $$S_{3}{\times Z_4\times Z_2}$$  S 3 × Z 4 × Z 2 symmetry which successfully accommodates the current active–sterile neutrino mixing in    $$3+1$$  3 + 1 scheme. The    $$S_3$$  S 3 flavor symmetry is supplemented by    $$Z_4\otimes Z_2$$  Z 4 ⊗ Z 2 symmetry to consolidate the Yukawa interaction of the model. The presence of    $$S_3\otimes Z_4\otimes Z_2$$  S 3 ⊗ Z 4 ⊗ Z 2 flavour symmetry plays an important role in generating the desired structure of the neutrino mass matrix. The model can reproduce the recent observed active-neutrino neutrino oscillation data for normal ordering in which two sterile–active mixing angles    $$\theta _{14, 24}$$  θ 14 , 24 get the best-fit values and the obtained values of    $$\theta _{34}, \delta _{14}, \delta _{14}$$  θ 34 , δ 14 , δ 14 , the sum of neutrino mass and the effective neutrino masses are within their currently allowed ranges.

$$3+1$$ active–sterile neutrino mixing in $$B-L$$ model with $$S_{3}{\times Z_4\times Z_2}$$ symmetry for normal neutrino mass ordering