  A new type of nonlocal currents (quasi-particles), which we call twisted
parafermions, and its corresponding twisted $Z$-algebra are found. The system
consists of one spin-1 bosonic field and six nonlocal fields of fractional
spins. Jacobi-type identities for the twisted parafermions are derived, and a
new conformal field theory is constructed from these currents. As an
application, a parafermionic representation of the twisted affine current
algebra $A^{(2)}_2$ is given.
