You're probably looking for a very specific niche—Harry refusing to help or rescue Ron usually pops up in stories where Harry is darker, more independent, or where his friendship with Ron is fractured. A lot of these are found on FanFiction.net, still a huge archive despite its age. You can try filtering for 'Harry Potter' and then using tags like 'Independent Harry' or 'Dark Harry' and sorting by favorites. The search function is clunky, so sometimes you have to wade through a lot. Archive of Our Own is way better for precise tagging. Look for tags like 'Harry Potter is Done with Everyone' or 'Not Ron Weasley Friendly'—those often lead to fics where Harry makes that choice. I found one called 'Antithesis' on AO3 where Harry basically lets Ron face consequences for a betrayal, but it's a whole AU.
Another place to check is specific forums or communities that focus on these power-dynamics. SpaceBattles and Sufficient Velocity forums sometimes host rationalist or more ruthless Harry stories where he wouldn't go out of his way for Ron. The writing style there tends to be more about logic and consequence, so the refusal feels calculated, not just emotional. Also, don't overlook older archives like SIYE, though they're more Hermione-centric; sometimes they have falling-out plots. Honestly, the trope isn't super common because a lot of writers love the trio dynamic, so when it happens, it's often a major plot point in longer fics about Harry forging a different path.