  We explore an interior solution of a physically symmetric vierbein with two
unknown functions in conformal teleparallel gravity. The field equations can be
described in a closed system for a particular form of the metric potentials and
an appropriate anisotropic function. As a result, we find a new set of
configurations consistent with observed pulsars. In particular, the boundary
conditions for the interior spacetime are used for the Schwarzschild spacetime
to constrain the conformal field that with a unit value through the surface of
a compact object. Furthermore, we apply the present model to the pulsar
$4U1608-52$ with approximated radius $R= 9.52 \pm 0.15$ km and mass $M= 1.74
\pm 0.14\, M_{\circledcirc}$. To analyze the stability, we also study the
causality conditions and the adiabatic index by assuming the
Tolman-Oppenheimer-Volkov equation, adiabatic index and the static state.
Moreover, the consistency of the model under consideration with other pulsars
is investigated.
