  In this study, we address the issue of a spherically symmetrical interior
solution to the quadratic form of $f\mathcal{(T)}=\mathcal{T}+\epsilon
\mathcal{T}^2$ gravitational theory using a physical tetrad that provides
vanishing components of the off-components of the field equation, in contrast
to what exists in the current literature. To be able to formulate the resulting
differential equation in a closed form, we employ the Krori-Barua (KB) ansatz.
Using the KB spacetime form, we derive the analytic form of the energy-density,
radial, and tangential pressures and the anisotropic form. All of these
quantities are affected by the dimensional parameter $\epsilon$, which causes
them to have a noted difference from those given in the frame of Einstein
general relativity. The derived model of this study exhibits a non-trivial form
of torsion scalar, and it also contains three constants that we drew from the
matching of the boundary condition with a line element that also features a
non-trivial form of torsion scalar. Having established the physical conditions
that are needed for any real stellar, we check our model and show in detail
that it bypasses all of these. Finally, we analyze the model's stability
utilizing the Tolman-Oppenheimer-Volkoff equation and adiabatic index and show
that our model satisfies these.
