  We extend the idea of conformal attractors in inflation to non-canonical
sectors by developing a non-canonical conformally invariant theory from two
different approaches. In the first approach, namely, ${\cal N}=1$ supergravity,
the construction is more or less phenomenological, where the non-canonical
kinetic sector is derived from a particular form of the K\"ahler potential
respecting shift symmetry. In the second approach i.e., superconformal theory,
we derive the form of the Lagrangian from a superconformal action and it turns
out to be exactly of the same form as in the first approach. Conformal breaking
of these theories results in a new class of non-canonical models which can
govern inflation with modulated shape of the T-models. We further employ this
framework to explore inflationary phenomenology with a representative example
and show how the form of the K\"ahler potential can possibly be constrained in
non-canonical models using the latest confidence contour in the $n_s-r$ plane
given by recent Planck and BICEP/Keck results.
