  We study several aspects of fillings for links of general quotient
singularities using Floer theory, including co-fillings, Weinstein fillings,
strong fillings, exact fillings and exact orbifold fillings, focusing on
non-existence of exact fillings of contact links of isolated terminal quotient
singularities. We provide an extensive list of isolated terminal quotient
singularities whose contact links are not exactly fillable, including
$\mathbb{C}^n/(\mathbb{Z}/2)$ for $n\ge 3$, which settles a conjecture of
Eliashberg, quotient singularities from general cyclic group actions and finite
subgroups of $SU(2)$, and all terminal quotient singularities in complex
dimension $3$. We also obtain uniqueness of the orbifold diffeomorphism type of
exact orbifold fillings of contact links of some isolated terminal quotient
singularities.
