This question already has an answer here:
Before this is marked as a duplicate, my question is more specific than the other one.
In the third book, when Harry has his wand on Black in the Shrieking Shack, he wants to kill him. He also clearly plans to use a spell because his wand was pointing at Black's heart, and when Crookshanks sits on Black's chest to protect him, Harry thinks:
So what if he had to kill the cat too? It was in league with Black.... If it was prepared to die, trying to protect Black, that wasn't Harry's business
If Harry was planning on using physical force to kill Black (which doesn't seem in character anyway - Harry bashing someone's head in?), he wouldn't worry about Crookshanks being in the way. And in that case, the cat's protection wouldn't make a difference anyway.
So if Harry was planning on using a spell, which one would he have used? Even if he knew about Avada Kedavra (which he doesn't until the next year), I doubt 13 year old Harry would be powerful enough for it to work. He didn't know Stunning, etc until next year, and he had no idea expelliarmus could knock someone out (the Snape incident happens later).
He seems very assured about killing Black. The only thing that seems to be getting in his way is his nerve. He seems like he knows what he wants to do.
"Harry raised his wand. Now was the moment to do it."
"-- but the footsteps were thundering up the stairs and Harry still hadn't done it."
"He hadn't done it. His nerve had failed him."
What spell could he have been thinking of, even if it may mot have ended working?