The static position correlation in a quantum Coulomb plasma near a wall is studied by means of a model where two quantum charges are embedded in a classical plasma at equilibrium. Three kinds of walls are considered: a wall without electrostatic properties, a dielectric, and an ideal conductor. At large separations y along the wall, the correlation exactly decays as 1/y^3, though no algebraic tail exists for classical charges near an ideal conductor. This tail originates from thermal statistical and purely quantum fluctuations of polarization clouds which are deformed by the geometric constraint due to the wall and by the charges induced by influence inside a wall with electrical properties. The coefficient of the 1/y^3 tail can be calculated explicitly in a weak-coupling and low-delocalization regime. Then classical, diffraction, and purely quantum contributions are disentangled.