  In this paper, we establish a vanishing theorem of Nadel type for the Witt
multiplier ideals on threefolds over perfect fields of characteristic larger
than five. As an application, if a projective normal threefold over
$\mathbb{F}_q$ is not klt and its canonical divisor is anti-ample, then the
number of the rational points on the klt-locus is divisible by $q$.
