We classify the central simple finite-dimensional noncommutative Jordan superalgebras of degree > 1 over an algebraically closed field of characteristic p > 2. The case of characteristic 0 was considered by the authors in the previous paper [24]. In particular, we describe Leibniz brackets on all finite dimensional central simple Jordan superalgebras except mixed (nor vector neither Poisson) Kantor doubles of the supercommutative superalgebra B(m, n).