We present a theoretical study on the equilibrium geometries, energetic, electronic, and magnetic characteristics of BGen (n = 1–20) clusters using the density functional theory (DFT) calculations. The most stable structures display a B atom located at the surface of BGen clusters, except for BGe9, 12, 16, 18, 19, 20. Larger clusters reveal higher binding energy, suggesting their greater stability compared to the corresponding Gen+1 clusters. The calculated fragmentation energy, second-order energy difference, and HOMO-LUMO energy gap reveal that the BGe9, 12 clusters are more stable than other cluster sizes. The calculated magnetic properties of the lowest-energy BGen clusters display a total spin magnetic moment equal to 1 μB, except for the BGe cluster, which takes the value 3 μB. These findings can be useful to the experimentalists in designing new Nano-catalytic systems.