  The celebrated Ohsawa--Takegoshi extension theorem for $L^2$ holomorphic
functions on bounded pseudoconvex domains in $\mathbb C^n$ is a fundamental
result in several complex variables and complex geometry. Ohsawa conjectured in
1995 that the same theorem still holds for more general bounded complete
K\"ahler domains in $\mathbb C^n$. Recently, Chen--Wu--Wang confirmed this
conjecture in a special case. In this paper we extend their result to the case
of holomorphic sections of twisted canonical bundles over relatively compact
complete K\"{a}hler domains in Stein manifolds. As an application we prove a
Hartogs type extension theorem for plurisubharmonic functions across a compact
complete pluripolar set, which is complementary to a classical result of
Shiffman and can be seen as an analogue of the Skoda--El Mir extension theorem
for plurisubharmonic functions -- a result that has been vacant since at least
1985.
