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In this work we propose an extension to the Standard Model in which weconsider the model 2HDM type-III plus massive neutrinos and the horizontalflavor symmetry $S_{3}$ $(\nu$2HDM$\otimes S_3)$. In the above framework andwith the explicit breaking of flavor symmetry $S_{3}$, the Yukawa matrices inthe flavor adapted basis are represented by means of a matrix with two texturezeroes. Also, the active neutrinos are considered as Majorana particles andtheir masses are generated through type-I seesaw mechanism. The unitarymatrices that diagonalize the mass matrices, as well as the flavor mixingmatrices, are expressed in terms of fermion mass ratios. Consequently, in themass basis the entries of the Yukawa matrices naturally acquire the form of theso-called {\it Cheng-Sher ansatz}. For the leptonic sector of $\nu$2HDM$\otimesS_3$, we compare, through a $\chi^{2}$ likelihood test, the theoreticalexpressions of the flavor mixing angles with the masses and flavor mixingleptons current experimental data. The results obtained in this $\chi^{2}$analysis are in very good agreement with the current experimental data. We alsoobtained an allowed value ranges for the "Dirac-like" phase factor, as well asfor the two Majorana phase factors. Furthermore, we study the phenomenologicalimplications of these numerical values of the CP-violation phases on theneutrinoless double beta decay, and for Long Base-Line neutrino oscillationexperiments such as T2K, NO$\nu$A, and DUNE.

On the lepton CP violation in a $\nu$2HDM with flavor