Let \( G = (V(G), E(G)) \) be a simple graph and let \( f \) be a function from \( V(G) \) to a subset of positive integers. An \( f \)-\({coloring}\) of \( G \) is a generalized edge-coloring such that every vertex \( v \in V(G) \) has at most \( f(v) \) edges colored with the same color. The minimum number of colors needed to define an \( f \)-coloring of \( G \) is called the \( f \)-\({chromatic\; index}\) of \( G \), and denoted by \( \chi_f'(G) \). The \( f \)-chromatic index of \( G \) is equal to \( \Delta_f(G) \) or \( \Delta_f(G) + 1 \), where \( \Delta_f(G) = \max \left\{ \frac{d(v)}{f(v)} \mid v \in V(G) \right\} \). \( G \) is called in the \({class-1}\), denoted by \( C_f1 \), if \( \chi_f'(G) = \Delta_f(G) \); otherwise \( G \) is called in the \({class-2}\), denoted by \( C_f2 \). In this paper, we show that the corona product of a cycle with either the complement of a complete graph, or a path, or a cycle is in \( C_f1 \).