  We apply geometric incidence estimates in positive characteristic to prove
the optimal $L^2 \to L^3$ Fourier extension estimate for the paraboloid in the
four-dimensional vector space over a prime residue field. In three dimensions,
when $-1$ is not a square, we prove an $L^2 \to L^{\frac{32}{9} }$ extension
estimate, improving the previously known exponent $\frac{68}{19}.$
