  The present paper is to deliberate the class of $3$-dimensional
trans-Sasakian manifolds which admits $\eta$-Einstein solitons. We have studied
$\eta$-Einstein solitons on $3$-dimensional trans-Sasakian manifolds where the
Ricci tensors are Codazzi type and cyclic parallel. We have also discussed some
curvature conditions admitting $\eta$-Einstein solitons on $3$-dimensional
trans-Sasakian manifolds and the vector field is torse-forming. We have also
shown an example of $3$-dimensional trans-Sasakian manifold with respect to
$\eta$-Einstein soliton to verify our results.
