It's about where Dumbledore calls two or three students from each house to help Percy Jackson and Camp Half-Blood in fighting the Titans (so it takes place in The Last Olympian). They gather in Dumbledore's office and start to read the Percy Jackson book series. Also, a Slytherin that attended was a child of Apollo.
Could this be Harry and Friends Read The Lightning Thief by Hoff of Slytherin?
Dumbledore summons Harry, Ron, Hermione and a few students from each House to his office:
I hope I didn't disturb anything important, because I had an urgent letter from a friend in America saying that he needs some Wizarding students to fight in a battle that will be coming up in a few months. I have selected a few students from each House that will accompany you on this journey.
There is mention of fighting the titans:
In the near future, there will be a big battle against the gods and the titans and one child of the Big Three gods will make a decision that will either save or destroy Mount Olympus.
Dumbledore reveals the Percy Jackson books:
"What I have called you all here for today is to learn about these heroes before you go to the camp that is located in America." Dumbledore pulled out a box that consisted of five books. The series was called "Percy Jackson and the Olympians."
And there is a Slytherin student who is a daughter of Apollo:
"Oh gods," Elaina Troy from Slytherin said. She knew Percy because she was his best mate. If they found out she was a daughter of Apollo, Elaina would go ballistic. No one but Draco knew. What if the story mentioned her? Elaina decided that she would tell them after they finished the book.