Harry Potter/Game of Thrones/A Song of Ice and Fire
SI is born into a Harry Potter AU to Voldemort and Bellatrix (nominally named Mordred Lestrange). Bellatrix is heavily pregnant when Voldemort gets blown up and so doesn't join in the torture party with the Longbottoms. Thanks to that she manages to avoid Azkaban.
The SI is in Ginny's class (one year below Harry).
Bellatrix has Sirius killed in prison so that her son inherits (oldest male child of the Black line when Sirius's grandfather dies in '91).
Mordred quite likes the prestige and power that comes with being Voldemorts son and heir but has no interest in letting daddy come back to life. A few not so subtle hints to Lucius gets him the Diary years before Hogwarts, he gets the Locket once he inherits the Black legacy (and that is the primary reason that he encouraged his mother to off Sirius), the Diadem when he attends Hogwarts, has access to the cup as the Lestrange heir, and can get the Ring fairly easily (Nagini wasn't made into a Horcrux until after Voldemort was resurrected).
Things are going pretty well for Mordred until the Twins happen to see Wormtail on the map and unveil him. Wormtail escapes and goes off to resurrect Voldemort (who is still anchored to Earth via Harry). Wormtail succeeds in his quest (to Mordred's displeasure).
Harry's Fifth year ends with Mordred managing to assassinate Dumbledore and get it blamed on Wormtail. He also manages to temper Voldemorts plans into a more casual and careful takeover, as without the Ministry fight the public still believes Voldemort to be dead.
Harry goes "on the run" that summer (in reality Mordred nabs him over the summer and keeps him under the Drought of Living Death in a trunk for the time being).
After Mordred graduates he ends up in charge of the Department of Mysteries (nepotism at its finest), and approximately a year later he Fiendfyre's Harry and engineers a situation to get Voldemort with him in the Death Chamber of the DoM. Mordred attempts to kill his now mortal father but, despite quite a lot of preparation, it ends up largely a draw and Mordred resorts to his final option.
The Deathly Hallows were made to interact with the Veil. The Cloak is attached to the interior of the veil and acts as a portal into Death's realm, the Wand acts as a key, and the Stone allows the bearer safe passage.
Mordred throws himself and Voldemort through the Veil, counting on his possession of the Stone to grant him safe passage while Voldemort gets stuck in Death's realm. It works but things don't go exactly as Mordred planned.
He pops out buck naked (save for the Stone) before a copy of the Veil buried at the heart of the Wall in Westeros. A veil that has the Cloak still attached but is lacking its Wand (and thus can't be used, nor can the Cloak be separated without the Wand).
The timing of Mordred's arrival is simultaneous with the Doom (not a coincidence, the Deathstick was in the Freehold and the source of most of their magic, and it reacted explosively to someone passing through the Veil).
Mordred has no knowledge of GoT/aSoIaF and figures that he is stuck. The fact that he lacks a wand (much less any other supplies) also greatly limits what he is capable of. Still, using even his limited abilities it is relatively easy for him to take over the Riverlands. Mordred has turned the Stone into his own Horcrux (although more in the vein of the Diary than the others, in that wearing it will result in Mordred's soul supplanting that of the wearer and adding their own abilities to his own) and by the time the Conquest comes along he has a handful of (relatively) mature Basilisks bound to his line (along with lots of other snake spies/assassins) and sits a secure throne (Legilmency makes deceiving him virtually impossible and his other abilities make assassination almost as difficult).
He cuts a deal with Aegon for Aegon's first daughter to marry Mordreds heir in exchange for the House of Slytherin's fealty.
When the Dance comes along (with Mordreds encouragement) he manages to bring down a dragon without anyone the wiser and thus (finally) has access to dragon heartstrings so that he can make a wand. It might not be a well fitted wand but it is a wand, and that is good enough to allow him to cast the spells needed to protect himself from the dangers of Valyria. Mordred spends the next great while plundering the Freeholds corpse.
Thoughts?