The global minimum Structures of pure and boron doped silver clusters up to 16 atoms are determined through ab initio calculations and unbiased structure searching methods. The structural and electronic properties of neutral, anionic, and cationic AgnB (n <= 1-5) and AgnB2 (n <= 14) clusters are much distinct from those of the corresponding pure silver. Considering that Ag and B possess one and three valence electrons, respectively, both the single and the double boron-atom doped silver clusters with even number of valence electrons are more stable than those with odd number of electrons, a feature also observed in the pure silver Clusters. We demonstrate that the species with a valence count of 8 and 14 appear to be magic numbers with enhanced stability irrespective of component or the charged State. A new putative global minimum structure of Ag-13(-) cluster, with high symmetry of C-2 nu, is unexpectedly observed as the ground state, which is lower in energy than the previous suggested bilayer structure.