Ab initio computed interaction forces are employed to describe the microsolvation of the A(2)(+)((2)Sigma) (A = Li, 2 Na, K) molecular ion in He-4 clusters of small variable size. The minimum energy structures are obtained by performing energy minimization based on a genetic algorithm approach. The symmetry features of the collocation of solvent adatoms around the dimeric cation are analyzed in detail, showing that the selective growth of small clusters around the two sides of the ion during the solvation process is a feature common to all three dopants.