In this paper two-stream instabilities in electron–positron–ion plasmas with quantum corrections are studied in both the linear and nonlinear regimes. The relative motion of ions with respect to electron–positron plasma and of positrons with respect to electron–ion plasma can give rise to such instabilities. Analytically and numerically the growth rates are calculated; the growth rates mainly depend on the quantum corrections and percentage concentration of different species. In the nonlinear studies, by employing the reductive perturbation technique, the Korteweg–de Vries (KdV) equation is derived; the KdV equation admits the solitary wave solution. The effect of streaming in the presence of quantum corrections on the amplitude and width of electrostatic soliton is studied. The conditions for hump-like and dip-like solitary structures are discussed.