By using the Vlasov-Poisson equations, we calculate an expression for the electrostatic potential caused by a test charge in an unmagnetized non-Maxwellian dusty plasma, whose constituents are the superthermal hot-electrons, the mobile cold-electrons with a neutralizing background of cold ions, and charge fluctuating isolated dust grains. The superthermality effects due to hot electrons not only modify the dielectric constant of the electron-acoustic waves but also significantly affect the electrostatic potential. The latter can be decomposed into the Debye-Hückel and oscillatory wake potentials. Analytical and numerical results reveal that the Debye-Hückel and wakefield potentials converge to the Maxwellian case for large values of superthermality parameter. Furthermore, the plasma parameters play a vital role in the formation of shielding and wakefield pattern in a two-electron temperature plasma. The present results should be important for laboratory and space dusty plasmas, where hot-electrons can be assumed to follow the non-Maxwellian distribution function.