Quantum black hole remnants and antimatter. Advanced physicists have worked out a quantum theory of gravity that has led them to understand how to make a quasi-stable quantum black hole remnant. The hole remnant weighs about a Planck mass (a few micrograms) so if it happens to explode the energy is only about what is in the gas tank of a car rather than, say, a nuclear bomb or an exploding planet.
The advantage of the hole remnant is that if you can shoot in bits of matter, they will form a mini mini black hole that instantly evaporates back out to a black hole remnant again. But half of the evaporating stuff ... can be antimatter! Hawking radiation is supposed to be a mix of both (and photons, which interconvert from matter + antimatter) So you can use this system to directly power a ship with matter as if it were antimatter. Or you can very carefully store up the antimatter in case you need to deploy a few photon torpedoes when you arrive for ... mining purposes.
I should note in response to the peanut gallery: the quantum black hole remnants are a catalyst received from some external source, possibly aliens. For example, let's suppose that the idea of primordial black holes is real. However, these were quite small and decayed a long time ago, leaving behind black hole remnants, some of which have not yet decayed. The aliens have let slip how to obtain them - perhaps they can be spotted with infrared studies of Saturn's rings and mined, or perhaps their cargo delivery drones passing near the Solar system have occasionally run into stray photon torpedoes left over from the mining operations.
Now how can matter possibly get into a black hole remnant, that is so much smaller than its own wavelength? Well, how does electron capture work? How does an NMR machine use a radio wave to ask an atomic nucleus which way it's spinning? Occasionally, the remnant just interacts with some kind of matter, perhaps the nucleus of a very heavy element that has the right kind of resonance in there somewhere. It momentarily takes up a nucleon, forming a higher-energy intermediate that is a black hole, before saying no, nevermind and giving the energy and/or mass back again with a random baryon number. The result is occasional antimatter-matter annihilation, not to mention fissioning some ordinarily stable isotope.
Now, some of the rubes who originally picked up these things were so entranced by having total conversion equipment in their starship that they didn't really look at the details. Heat up a reaction chamber, use a heat engine to extract limitless energy from tiny amounts of matter, use it to run an ion drive. We're talking large, bulky jalopies there.
But if you want to build a proper flivver, you need decently strong radio broadcast equipment to orient your nuclear spins properly, as well as a UV module to orient your catalyst. Then you build your reaction chamber out flat, with a very thin wall so that your gammas radiate to space. With the right magnetic field setting, you can have tolerable settings for these resonances and control the emission patterns of your antiparticles so that when they annihilate the gammas usually go the right way. Since much of the propulsion here is a photon drive, one of these needs more quantum remnant catalyst for the same thrust. You have to recycle your plates more often to recover catalyst. But you need essentially no moving parts - it's a very simple system to use and maintain. The ships can be tiny and maneuverable, in case you need to avoid running into any photon torpedoes.
