  Non-interacting particles obeying certain fractional statistics have been
predicted to exhibit superconductivity. We discuss the issue in an attractively
interacting system of spinful semions on a lattice by numerically investigating
the presence of off-diagonal long-range order at zero temperature. For this
purpose, we construct a Hubbard model wherein two semions with opposite spin
can virtually coincide while maintaining consistency with the fractional
braiding statistics. Clear off-diagonal long range order is seen in the strong
coupling limit, consistent with the expectation that a pair of semions obeys
Bose statistics. We find that the semion system behaves similarly to a system
of fermions with the same attractive Hubbard $U$ interaction for a wide range
of $U$, suggesting that semions also undergo a BCS to BEC crossover as a
function of $U$.
