  Let $V$ be a vertex operator algebra, $T\in \mathbb{N}$ and $(M^k, Y_{M^k})$
for $k=1, 2, 3$ be a $g_k$-twisted module, where $g_k$ are commuting
automorphisms of $V$ such that $g_k^T=1$ for $k=1, 2, 3$ and $g_3=g_1g_2$.
Suppose $I(\cdot, z)$ is an intertwining operator of type $({array}{c} M^{3}
M^{1} M^{2} {array}) $. We construct an $A_{g_1g_2}(V)$-$A_{g_2}(V)$-bimodule
$A_{g_1g_2, g_2}(M^1)$ which determines the action of $M^1$ from the bottom
level of $M^2$ to the bottom level of $M^3$ and explored its connections with
fusion rules.
