alt Hacker News> `void*` is frequently clearer - it's a signal that it's an opaque blob at this point in the code, and that something else will try to give it meaning later.
And that's fine, until something else gives it the wrong meaning later. If you're just plumbing, and you're pumping around opaque blobs, if somewhere in the plumbing you connect the wrong source to the wrong destination, you get no warning.
Yes, in this case, void* is kind of smelly. If the intent of your function is to receive a const struct MyCustomData*, then that should be the type of the argument. If you later need to handle a const struct MyOtherCustomData*, you can add an overload that takes that argument. Or use a template as others pointed out. Use the type system to help you, so you're warned if you try to pass the method const struct BadCustomData* by accident.
If you truly don't know what the underlying structure of the "blob" of data is, sure, go ahead and use void* and explicitly convert the pointer type when you know what it is, but at least add a comment that you're entering the danger zone.