  The first purpose of this paper is to solve completely the finite field cone
restriction conjecture in four dimensions with $-1$ non-square. The second is
to introduce a new approach to study incidence problems via restriction theory.
More precisely, using the cone restriction estimates, we will prove sharp
point-sphere incidence bounds associated with complex-valued functions for
sphere sets of small size. Our incidence bounds with a specific function
improve significantly a result given by Cilleruelo, Iosevich, Lund,
Roche-Newton, and Rudnev.
