However, Jason Todd becomes the villain Red Hood after his death and resurrection, and he does fight Batman in several comics, most notably in the "Under the Hood" storyline.
This storyline takes place in Batman #635-650 and Robin #126-130. It's a pivotal story in the Batman mythos, exploring the complex relationship between Batman and Jason Todd, and the consequences of Jason's traumatic past.
If you're interested in seeing their fight, I recommend checking out these issues.