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Using the bases of principal subspaces for twisted affine Lie algebras except$A_{2l}^{(2)}$ by Butorac and Sadowski, we construct bases of the highestweight modules of highest weight $k\Lambda_0$ and parafermionic spases for thesame affine Lie algebras. As a result, we obtain their character formulasconjectured in arXiv:math/0102113.

Parafermionic bases of standard modules for twisted affine Lie algebras of type $A_{2l-1}^{(2)}$, $D_{l+1}^{(2)}$, $E_6^{(2)}$ and $D_4^{(3)}$