  In this paper, we construct a large class of new simple modules over the
twisted $N=2$ superconformal algebra. These new simple modules
  are restricted modules based on the simple
  modules over certain finite-dimensional solvable Lie superalgebras, including
various versions of Whittaker modules. We elaborate that they are also the
twisted modules for the universal $N=2$ superconformal vertex algebra. On the
other hand, we give an explicit characterization of the simple restricted
modules over the twisted $N=2$ superconformal algebra $\mathcal{T}$ under the
condition that $T_t$ in $\mathcal{T}$ acts injectively for some $t\in
\frac{1}{2}+\Z_+$.
