We determine exactly the short-distance effective potential between two "guest" charges immersed in a two-dimensional two-component charge-asymmetric plasma composed of positively (q1 = +1) and negatively (q2 = -1/2) charged point particles.The result is valid over the whole regime of stability, where the Coulombic coupling (dimensionless inverse temperature) β < 4. At high Coulombic coupling β > 2, this model features like-charge attraction.Also, there cannot be repulsion between opposite-charges at short-distances, at variance with large-distance interactions.