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

On the finite field cone restriction conjecture in four dimensions and applications in incidence geometry