  We investigate the possibility to construct extended parafermionic conformal
algebras whose generating current has spin $1+\frac{1}{K}$, generalizing the
superconformal (spin 3/2) and the Fateev Zamolodchikov (spin 4/3) algebras.
Models invariant under such algebras would possess $Z_K$ exotic supersymmetries
satisfying (supercharge)$^K$ = (momentum). However, we show that for $K=4$ this
new algebra allows only for models at $c=1$, for $K=5$ it is a trivial
rephrasing of the ordinary $Z_5$ parafermionic model, for $K=6,7$ (and,
requiring unitarity, for all larger $K$) such algebras do not exist.
Implications of this result for existence of exotic supersymmetry in two
dimensional field theory are discussed.
