  Topological defect lines (TDLs) are extended line operators which act on the
Hilbert space of two-dimensional CFTs and satisfy non-trivial fusion algebras
when forming junctions. Among the most interesting fusion algebras are the
so-called Tambara-Yamagami (TY) fusion categories which are realized in
(bosonized) Parafermionic CFTs. The corresponding TY[$\mathbb{Z}_k$]-categories
have been explicitly realized for the cases $k=2$, $k=3$, and $k=4$ together
with the action of the defect lines on the Hilbert space of the corresponding
CFTs. For each of the cases, different methods have been used in the previous
literature. In the current paper, we present a unified framework for finding
the TDLs in bosonized Parafermionic CFTs. Our approach relies on combining
several previously used methods and the definition of an extended $S$ matrix.
We apply the method to the cases $k=2$ to $k=5$ to extract corresponding TDL
fusion algebras.
