  We study topological defect lines (TDLs) in two-dimensional $\mathbb
Z_N$-parafermoinic CFTs. Different from the bosonic case, in the 2d
parafermionic CFTs, there exist parafermionic defect operators that can live on
the TDLs and satisfy interesting fractional statistics. We propose a
categorical description for these TDLs, dubbed as ``para-fusion category",
which contains various novel features, including $\mathbb Z_M$ $q$-type objects
for $M\vert N$, and parafermoinic defect operators as a type of specialized
1-morphisms of the TDLs. The para-fusion category in parafermionic CFTs can be
regarded as a natural generalization of the super-fusion category for the
description of TDLs in 2d fermionic CFTs. We investigate these distinguishing
features in para-fusion category from both a 2d pure CFT perspective, and also
a 3d anyon condensation viewpoint. In the latter approach, we introduce a
generalized parafermionic anyon condensation, and use it to establish a functor
from the parent fusion category for TDLs in bosonic CFTs to the para-fusion
category for TDLs in the parafermionized ones. At last, we provide many
examples to illustrate the properties of the proposed para-fusion category, and
also give a full classification for a universal para-fusion category obtained
from parafermionic condensation of Tambara-Yamagami $\mathbb Z_N$ fusion
category.
