The Genii A-bomb was a nuclear weapon used by the Genii.
The original shielding of the bomb was minimal. This aside, their hope was that if they could place them inside a Hive ship, an interior detonation would be capable of destroying a Wraith Hive ship. It was initially hoped that the Atlantis expedition and the Genii could enter into an alliance to perfect the bombs, but the Genii attempt to betray Lt. Colonel John Sheppard's team for a Gateship and their subsequent attempt to take control of Atlantis ended this plan. (ATL: "Underground")
During the Battle of Atlantis, the Genii give the Atlantis expedition two of their bombs and in exchange received C-4 and some of their medicines. Dr. Elizabeth Weir convincing the Genii to do so by arguing that this test allowed the Genii to see how their bombs performed in battle without putting themselves at risk. Sheppard was able to use at least one to destroy a Hive ship by piloting a cloaked Jumper armed with the bomb inside (he later used a similar tactic to destroy the Super-hive), surviving due to the Daedalus beaming him out. It is unknown what happened to the second bomb. (ATL: "The Siege, Part 2", "The Siege, Part 3")
Later, Ladon Radim used one as part of his coup. He built it, planted it on an abandoned planet under a warehouse and tricked Cowen and his elite guard there. The bomb killed Cowen and his guard, allowing Ladon to overthrow the government and become the new leader of the Genii. (ATL: "Coup D'etat")