  In this paper, we investigate the minimal symplectic fillings of small
Seifert 3-manifolds with a canonical contact structure. As a result, we
classify all minimal symplectic fillings of small Seifert 3-manifolds
satisfying certain conditions. Furthermore, we also demonstrate that every such
a minimal symplectic filling is obtained by a sequence of rational blowdowns
from the minimal resolution of the corresponding weighted homogeneous complex
surface singularity.
