  By using Bogoliubov-de Gennes (BdG) equations, we study superconducting (SC)
states in a quasi 2-dimensional system of radius $R$. It is shown that no
vortices exist in s-wave SC samples with $R<R_\text{c}\sim\xi(0)$, the T=0
coherence length. We predict that chiral p-wave states exhibit
superconductivity for $R<R_\text{c}$ only in the presence of a vortex with
opposite chirality. This {\it induced} SC phase is a consequence of non-zero
chirality of the pairing order parameter and implies the presence of chiral
edge currents. Our study may be applied to sharply probing the pairing symmetry
of unconventional superconductors.
