  We extend the splitting operation from binary matroids (Raghunathan et al.,
1998) to $p$- matroids, where $p$-matroids refer to matroids representable over
$GF(p).$ We also characterize circuits, bases, and independent sets of the
resulting matroid. Sufficient conditions to yield Eulerian $p$-matroids from
Eulerian and non-Eulerian $p$-matroids by applying the splitting operation are
obtained. A class of connected $p$-matroids that gives connected $p$-matroids
under the splitting operation is characterized.
