  In this paper, for a vertex operator algebra $V$ with an automorphism $g$ of
order $T,$ an admissible $V$-module $M$ and a fixed nonnegative rational number
$n\in\frac{1}{T}\Bbb{Z}_{+},$ we construct an $A_{g,n}(V)$-bimodule
$\AA_{g,n}(M)$ and study its some properties, discuss the connections between
bimodule $\AA_{g,n}(M)$ and intertwining operators. Especially, bimodule
$\AA_{g,n-\frac{1}{T}}(M)$ is a natural quotient of $\AA_{g,n}(M)$ and there is
a linear isomorphism between the space ${\cal I}_{M\,M^j}^{M^k}$ of
intertwining operators and the space of homomorphisms
$\rm{Hom}_{A_{g,n}(V)}(\AA_{g,n}(M)\otimes_{A_{g,n}(V)}M^j(s), M^k(t))$ for
$s,t\leq n, M^j, M^k$ are $g$-twisted $V$ modules, if $V$ is $g$-rational.
