  In superconductors, the condensation of Cooper pairs gives rise to fluxoid
quantization in discrete units of $\Phi_0 = hc / 2e$. The denominator of $2e$
is the signature of electron pairing, which is evidenced by a number of
macroscopic quantum phenomena, such as the Little-Parks effect and the
Josephson effect, where the critical temperature or the critical current
oscillates in the period of $\Phi_0$. Here we report the observation of
fractional Little-Parks effect in mesoscopic rings of epitaxial
$\beta$-Bi$_2$Pd, a topological superconductor. Besides $\Phi_0$, novel
Little-Parks oscillation periodicities of $2\Phi_0$, $3\Phi_0$ and $4\Phi_0$
are also observed, implying quasiparticles with effective charges being a
fraction of a Cooper pair. We show that the fractional Little-Parks effect may
be closely related to the fractional Josephson effect, which is a key signature
of chiral Majorana edge states.
