  NaAlSi is a quasi-two-dimensional semimetal with superconductivity below Tc =
6.8 K and a band structure characterized by nodal lines near the Fermi level
and potential topological surface states. Electrical resistivity measurements
on its superconducting transitions in magnetic fields were made using
plate-like single crystals. In the magnetic field-temperature phase diagram, we
observed a substantial reduction in resistivity in a pre-transitional zone
above the bulk superconducting regime only when the magnetic fields were
perpendicular to the plane, rather than parallel to it. Significant sample
(thickness) dependence, reentrant behavior, and sensitivity to electrode
configurations all indicate that a portion of the crystal has an upper critical
field greater than the bulk superconductivity in the pre-transitional region.
This fractional superconductivity may occur on the side surface of the crystal.
