  The flavour problem and the viability of texture zeros of the Majorana mass
matrix in the 3+1 active-sterile neutrino mixing scenario are investigated in
this work using a novel bottom-up technique where we leverage the pertinent
concepts of full modular group, modular invariants, and $A_4$ flavour symmetry
as theoretical tools for the explicit construction of neutrino models. In this
approach we treat each chiral field as modular forms in the 3+1 neutrino mixing
which are constrained by the $A_4$ modular symmetry. Using these techniques, we
create straightforward predictive models that only depends on a few parameters
and simultaneously explains the observed pattern of neutrino mixing without the
need for fine-tuning, allowing us to perceive the feasible zero textures of the
Majorana mass matrix under the 3+1 framework.We discuss the implications of the
allowed 3+1 zero textures by analyzing the sterile neutrino parameters,
providing insight into the flavor problem and the viability of the Majorana
mass matrix. The values of the active-sterile mixing (ASM) parameters predicted
from our models are highly consistent with the $3\sigma$ values of the ASM
parameters.
