  When in general geometric backgrounds the metric is accompanied by torsion,
the metric conformal properties should correspondingly be followed by analogous
torsional conformal properties; however a combined metric torsional conformal
structure has never been found which provides a curvature that is both
containing metric-torsional degree of freedom and conformally invariant: in
this paper we construct such a metric-torsional conformal curvature. We proceed
by building the most general action, then deriving the most general system of
field equations; we check their consistency by showing that both conservation
laws and trace condition are verified. Final considerations and comments are
outlined.
