Maybe the question is too general, let me give some examples.

1. When you want to insert custom code changes, where do you put them?
2. Where to put custom resources like fonts, for example?
3. Does psx games use function like the c function alloc?

For Policenauts, I used the font file as well.  It stayed static in memory the whole time, so I just overwrote the end of it with my new assembly.  In my case, the font was in a separate file than the SLPS file, so it was very easy.

If that's not possible (ie, the game uploads the font to VRAM and forgets about it and doesn't have lots of useless stuff either), there are also some methods that need a bit more work.
A PSX game is like any normal program, it allocates and frees memory as it needs to. Where these functions are is up to the game though. If you can't overwrite/extend some other file in RAM, you could also just load a completely new file. Most games probably have a function that loads a file/subfile to RAM and returns a pointer to it. If you do that right at the beginning, you can load your code and it will be at that space without taking much away from the available RAM.
You'd have to find that function yourself though, and you'd also need a small area to save your loader.