Abstract Texture zeros in fermion mass matrices have been widely considered in tackling the Standard Model flavour puzzle. In this work, we perform a systematic analysis of texture zeros in lepton mass matrices in the framework of Γ 3 ′ ≅ T ′ $$ {\Gamma}_3^{\prime}\cong {T}^{\prime } $$ modular symmetry. Assuming that the lepton fields transform as irreducible representations of T′, we obtain all possible texture-zero patterns for both charged-lepton and neutrino mass matrices which can be achieved from T′ modular symmetry. We provide representative models for the phenomenologically-viable textures which can accommodate the experimental data. The predictions for lepton mixing angles, CP-violating phases, light neutrino masses and effective neutrino mass relevant for neutrinoless double beta decay, are discussed. We find that the minimal viable lepton model depends on only 7 real free parameters including the modulus τ (the corresponding charged-lepton mass matrix contains 4 vanishing entries, and the neutrino mass matrix has 1 texture zero). Finally, we study in detail three benchmark models, one for each neutrino mass generation mechanism considered (Dirac, Majorana via Weinberg operator and Majorana via minimal type-I seesaw mechanism).
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