Suppose, instead of molecules and atoms existing, there was only prime matter and types of prime matter. So there would be steel type of prime matter, flesh type of prime matter, etc.... How would physics work out in this universe? Ard there any science fiction books about this?
Let’s ask the opposite question, what would it mean for matter to not be continuous: it would mean that there is a void.
Now, the original atomists argued that their atoms moved within a void, however Aristotle argues against this, he pointed out that there void was not in fact a void, but place and he speculated on the notion of place having a kind of potency, this has a family resemblance to the notion of a field: a field has places with potency.
Hence, Aristotle affirmed, along with Parmenides, that void is not. Similarly, Newton and Einstein. Newton explicitly in arguing against gravity being a force at a distance but was unable to come up with a theory; and Einstein implicitly in finding the mechanism and then in arguing against the phenomena of non-locality in entangled quantum systems. (Various experiments, following an argument of Bell, have shown that this non-locality is an explicit feature of QM).
We can then see our world as as a continuum of continua. Or as Carlos Rovelli put it in his textbook on Quantum Gravity, the world is simply fields upon fields.
Einstein's resolution of Brownian Motion was the first serious estimate of the size of an atom, and so first really definitive evidence they exist. Even after the turn of 1900 some leading physicists like Ernst Mach were not even considering the atomic hypothesis to be seriously viable; and the scorn Boltzman recieved for his wotk on entropy that supported it may have contributed to his depression and suicide.
The previous paradigm was continuum mechanics, and all classical mechanics is implicitly based on it. Quantum mechanics puts a discrete size limit on the smallest possible probe, the lowest energy interaction with a system, and it's peculiar nature follows from that. So, you could argue, continuous matter would look like the classical physics world. Perhaps the biggest problem with that would be problems with radiating heat, the 'ultraviolet catastrophe', where as bodies get hotter they lose their heat very rapidly. Other impacts are quite subtle & small scale.
You seem to be asking about a specific model, something like Aristotle's physics, where there are different types of continuous substances, with different principles, which intermingle in various ways? Aristotle felt he lived in such a world, so again you could say, like he described. This might seem flippant, but we should remember our own models are also very much approximations, rooted in our own experiences, and though we expect consiliance of evidence and new theories to encompass and generalise old ones, we are still a long way from 'real reality'; and Hawkinv argued from Godel's Theorems the goalposts for that will alwsys shift.
Our best current theory, indeed it can be argued the best theory humans have ever developed in terms of accuracy and scope, is quantum field theory. The fields in this are in a sense continuous, with for instance quantum jumps recognised as transitions between states like different standing waves. You could say that QFT is a kind of continuum theory, of continuous fields. It depends how you define 'matter', as having inertia (Higgs field), or only as having mass which all energy has.
Lastly, the main candidate for uniting gravity with QFT, M Theory, implies our universe and it's timeline are only subsets of a vast 11 dimensional landscape of probabilities. It's hard to grapple with that, but it can be pictured as making continuities of variations in apparently discrete things like events and timelines.
The only possibly relevant scifi I can think of is Asimov's The Gods Themselves. In this beings from the end of the (stelliferous era of the) universe when the last stars are going out and the fundamental constants of nature have changed, start to influence our own time. Those aliens exist as continua which can intermingle with each other and matter around them. They are among the most alien but compelling aliens I know of in SF.