In this study, we explore the Finch-Skea perfect fluid solution and
extend its domain to three distinct anisotropic interior models
within the framework of $f(\mathbb{R},\mathbb{T})$ theory,
incorporating the influence of an electromagnetic field. We assume a
static spherical spacetime initially coupled with an isotropic
matter distribution. We then introduce a Lagrangian corresponding to
an additional gravitating source, taking into account its role in
inducing pressure anisotropy within the original fluid source. By
deriving the field equations for the combined matter setup, we apply
a radial component transformation, yielding two distinct systems of
equations. Also, we consider a charged exterior spacetime to
determine three constants associated with the Finch-Skea solution at
the boundary. Our findings suggest that, under certain parametric
choices, all three resulting models exhibit physical relevance
within this modified theory.