  We study the Kondo screening effect generated by a single-electron transistor
or quantum dot embedded in a small metallic ring. When the ring circumference
$L$ becomes comparable to the fundamental length scale $\xi_K^0=\hbar \upsilon
_F/T_K^0$ associated with the {\it bulk} Kondo tempe the Kondo resonance is
strongly affected, depending on the total number of electrons ({\it modulo} 4)
and magnetic flux threading the ring. The resulting Kondo-assisted persistent
currents are also calculated in both Kondo and mixed valence regimes, and the
maximum values are found in the crossover region.
