In this paper we study the fractional SchrödingerâPoisson system Δ2s(âÎ)su+V(x)u=Ï|u|2s*â3u+|u|2s*â2u,Δ2s(âÎ)sÏ=|u|2s*â1,xâR3, where s â (0, 1), É > 0 is a small parameter, 2s*=63â2s is the critical Sobolev exponent and VâL32s(R3) is a nonnegative function which may be zero in some regions of R3, e.g., it is of the critical frequency case. By virtue of a new global compactness lemma, and the LusternikâSchnirelmann category theory, we relate the number of bound state solutions with the topology of the zero set where V attains its minimum for small values of É.