A/N - All the characters and locations that appeared in the books belong to J.K. Rowling. Anything you don't recognize probably belongs to me. This is probably going to be a multi-chapter story, but don't hold your breath.
The Sorting Hat's Choice
"Potter, Albus," Professor Longbottom called out.
Albus heard whispering break out all along the four House tables. He couldn't make out the words, but he knew what they'd be saying. Potter? Did he say Potter? One of the Potters? James said they'd stared and whispered when he first arrived at Hogwarts too, but James loved attention. Albus wished he was a ghost so he could sink through the floor. Instead he walked forward on trembling legs and took his place on the stool. Neville gave him a reassuring wink and whispered for Albus's ears alone, "It'll be fine, Al. The Hat always knows where you belong."
But what if I belong in Slytherin? Albus wanted to ask. Would Dad and Mum really not care if I was in the same House as the wizard who murdered my grandparents? Would James want a Slytherin for a Potter? What if I belong in Slytherin because I'm not really a Potter? Before he could ask any of these questions, the hat fell over his eyes.
For a moment he sat in darkness and silence. Then a voice spoke in his ear. It was a wheezy voice, and Albus pictured a very old, stooped wizard with shrewd eyes. "Another Potter, eh?" the Hat said. "Each of you is trickier than the last. You're not lacking intelligence, nor courage. Plenty of loyalty, and a rebellious streak as well. Why you'd excel almost anywhere? Do you have a preference?"
Albus's heart leapt. Dad had been right. You could choose. He'd thought maybe the Hat only did that in special cases like the Chosen One. Wanting to be sure before he said anything he couldn't take back, Albus thought, You'll put me anywhere I want? Anywhere at all?
"Oh, yes," said the Hat. "Like I say, you'll excel no matter where you go. Now, as to what you'll excel at, don't ask me. I'm a hat. I can only see what's in your head."
Albus thought it over. The Hat waited patiently, humming tunelessly to itself. If he chose Gryffindor, Albus thought, he'd be with James and Rose and almost all of his cousins. But that wouldn't necessarily be a good thing. Ravenclaw might not be too bad. Louis and Victoire were in Ravenclaw, and he did like books. He didn't know anyone in Hufflepuff, but that had been Teddy's house and he'd said it was the best. And Slytherin … Well, hadn't Dad said the bravest man he ever knew was a Slytherin? If Albus was a Slytherin at heart, he wouldn't really fit in anywhere else, would he?
He took a deep breath. "Just put me where I belong," he said aloud.
"Good choice," said the hat, and then it shouted for the whole hall to hear, "HUFFLEPUFF."
Professor Longbottom swept the Hat off Albus's head and gave him an encouraging smile. Albus walked down to the Hufflepuff table which was shouting and cheering as though they'd won a Thousand Galleon Prize Draw. A group of third years was chanting, "We got a Potter! We got a Potter!" Albus caught a glimpse of James sitting two tables over with the rest of Gryffindor. He looked like he'd taken a Bludger to the head. Albus gave him an apologetic shrug and took his place with his House.