Complementary legs and symplectic rational balls

We completely characterize when a small Seifert fibered space with complementary legs symplectically bounds a rational homology ball in the case $e_0\leq -1$, and we establish strong obstructions for other values of $e_0$. Our results highlight a sharp contrast with the smooth category, where many more such Seifert fibered spaces are known to bound smooth rational homology balls. We also complete the classification of contact structures on spherical $3$-manifolds with either orientations that admit symplectic rational homology ball fillings.