Ab initio calculations on ZnSe quantum dots (QDs) doped with one Mn atom predict a new nonstoichiometric magnetic magic Zn11MnSe13 structure in contrast to QDs of undoped ZnSe that are stoichiometric and exhibit magic behavior for ZnnSen with n = 13 and 34. Our results suggest that such doping would lead to a high abundance of only one specie (the magic QD) that would be produced preferentially. The stoichiometric Zn n-1MnSen QDs have a large magnetic moment of 5 $\mu$B that is predominantly localized on the Mn site. However, nonstoichiometic QD has a reduced magnetic moment of 3 $\mu$B due to strong covalent bonding of the Mn atom with the excess Se atom and a small gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). Charging this magic QD with two electrons leads to a large HOMO-LUMO gap of 1.8 eV and 5 $\mu$B magnetic moment. These results together with calculations on Mn-doped n = 34 QD provide a possible growth mechanism of larger doped QDs and a new ground for understanding such QDs of compound semiconductors. {\textcopyright} 2011 American Physical Society.