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In this paper, we consider the following quasilinear Schrödinger–Poisson system with exponential and logarithmic nonlinearities −Δu+ϕu=|u|p−2ulog|u|2+λf(u),inΩ,−Δϕ−ε4Δ4ϕ=u2,inΩ,u=ϕ=0,on∂Ω, where are parameters, is a bounded domain, and has exponential critical growth. By adopting the reduction argument and a truncation technique, we prove for every , the above system admits at least one pair of nonnegative solutions for large. Furthermore, we research the asymptotical behavior of solutions with respect to the parameters and . The novelty of this system is the intersection among the quasilinear term, logarithmic term, and exponential critical term. These results are new and improve some existing results in the literature.