Sirius is free after the third year, as Pettigrew never escaped after Snape delivered him to Dumbledore while Lupin transformed. Both Lily and James were assassins, and Harry finds out when Sirius takes Harry to the Potter family vault. Now for the 'warnings', (more like I'm weird and am including my weirdness here) this is going to have a lot of comfort, as this is more a combination of the two worlds, and if you combine them right, you don't have to keep reminding us that the Assassins are here, so this is just like a combination of Harry/Sirius comfort, Harry/Hermione comfort which leads to eventual romance, AC crossover fic, abuse (from the Dursleys), and many more, so I implore you to keep reading if you hit a snag where your like wait wtf? Sorry for the long introduction, I just want to make myself clear on my current ideas for this little series thing, I'm sure there will be many more like it.
EDIT #1: Based on the movies, although that shouldn't affect reading, it's more to get a visualization of the characters. Rating it M now because it may take a turn in the rape direction and I don't feel like forgetting it later if it does.

Harry's mind was racing, Sirius Black had just dragged Ron down the Whomping Willow, into the Shrieking Shack, where they found out that it was not Sirius who betrayed the Potters, but Ron's rat, or what they thought was a rat, as it was Peter Pettigrew, disguised as a rat after Sirius confronted him, 13 years ago. When Snape had confronted them, Harry knocked him out and demanded the truth from Lupin and Sirius. When he got it, his godfather, DADA teacher, and Pettigrew (along with Ron and Hermione of course) left from the Whomping Willow, where Sirius asked Harry if he would like to live with him, and Harry happily, and immediately accepted. Sirius was a bit frightened by this, wondering where he was living currently to give it up quickly, but he didn't have much time to ponder that from both his own excitement and the fact that Lupin was transforming.

The timing was perfect as Severus stormed up through the Whomping Willow passage, to see that Lupin was transforming and the damned rat looked about ready to bolt.

"Black, you deal with Potter and his entourage, I will handle this vermin," he said, pointing to Pettigrew. Quickly, Severus grabbed Peter and put his hands behind his back and rushed him up to the castle, eventually deciding Petrificus Totalus would do the job much easier and much more, risk free. Meanwhile, in an attempt to get his best friend werewolf off of their tail, he transformed, but Harry pursued after him. Thanks to (future) Hermione distracting Lupin, Harry rushed down the hill Sirius had fallen, leading him (and an unconscious Sirius) to the edge of the Black Lake, where there were hundreds, maybe thousands of Dementors. The last thing Harry remembered was a stag and his… Dad?

Meanwhile, future Harry and Hermione saved themselves multiple times before reaching the Black Lake and waiting for Sirius and Harry to arrive (this stuff gets really complicated so just stick with me, or don't, it's literally just the movie scene with a bit more fluff when Harry and Hermione talk).

"It was my dad- who conjured the Patronus, I know it was, I saw him," Harry stated, Hermione looked quizzically at him before saying, "Harry but your dads-"

"dead, I know, but he'll come, I saw him, I know he will." Hermione looked at him, sad. She didn't have a clue what Harry saw, but something told her it was not his dad. Harry then began to talk about how Sirius offered for Harry to stay with him, and Harry began to talk about all of the things he wanted to show Sirius and how he wanted to get a house in the countryside where he could see, well, life, the trees, the sun setting every night. It was then Hermione realized how truly caring Harry was. He wasn't just thinking about how Sirius was helping him by taking him in, he was thinking of all of the ways he could help Sirius. She knew how much he cared about everything related to his parents. During a particular night when Harry was upset over not only his parents but also Ron being jealous, Harry told Hermione he'd give every last galleon, knut, and sickle in his Gringotts account if he could only see his parents for a second.

Hermione hugged Harry tightly, letting him know he was certainly not alone, now especially with Sirius in the picture. Unfortunately, Dementors began to soar through the air, and they turned their attention to the two bodies on the opposite shore of the lake. Harry excitedly (which turned to worriedly) waited for his dad to show up. Every second that the air remained still Harry became more and more scared, more and more upset. Finally, Harry couldn't take seeing a Dementor that close to Sirius, and the sprinted towards the shore, coming to a halt and yelling, "EXPECTO PATRONUM!". From there he cast the biggest Patronus he'd ever seen, stopping when the Dementors began to flee.

From there, you know the rest, until you don't. Sirius met a now pleading Peter and a happy but worn Lupin in Dumbledore's office, where Dumbledore explained the situation to Fudge, who set up a case that could be done by tomorrow.

And that's the first chapter down, sorry there's no, well new stuff, aside from Pettigrew being caught there's not much I changed, which I apologize for, I just felt that it was important to try and relive this little section before jumping into the story. The next chapter briefly goes into closing Sirius's trial and jumping into some assassin stuff.