I'm looking for possible sources of energy that could one day replace fusion.
I'm not necessarily looking for cool sounding names, as I'm trying to avoid technobabble, but ones that could somewhat be defended as possible replacements with a bit of real science.
Have you heard about mass-energy equivalence? It states that mass is equivalent to raw energy, and energy to mass in this formula: $$E = mc^2$$ That means that each gram of matter has 89,875,517,873,681,764 Joules of energy, that is, 90 petajoules.
Annihilate a gram of matter with a gram of antimatter would release all that amount of energy. Fusion and fission already do this, but at lower efficiency (since not all mass is turned into energy).
From wikipedía:
Hawking radiation reduces the mass and rotation energy of black holes and is therefore also known as black hole evaporation. Because of this, black holes that do not gain mass through other means are expected to shrink and ultimately vanish. Micro black holes are predicted to be larger emitters of radiation than larger black holes and should shrink and dissipate faster.
[...]
Hawking showed that quantum effects allow black holes to emit exact black-body radiation. The electromagnetic radiation is produced as if emitted by a black body with a temperature inversely proportional to the mass of the black hole.
Basically, as less mass a black hole as (and so smaller it is), more energy it produces.
I don't want to explain how that works, but in the title link you can see the explanation.
Using this online calculator we know that a black hole of 1,000 kg would emit $3.56 \times 10^{26} W$, and last $8.4 \times 10^{(-8)} \text{ seconds}$. A black hole of 1,000,000 kg would emit $3.56 \times 10^{20} W$, but last $84 \text{ seconds}$.
Hawking radiation has a 100% mass-energy equivalence, more than fusion (less than 4%, citation needed).
From wikipedía:
Physics currently lacks a full theoretical model for understanding zero-point energy; in particular the discrepancy between theorized and observed vacuum energy is a source of major contention. Physicists Richard Feynman and John Wheeler calculated the zero-point radiation of the vacuum to be an order of magnitude greater than nuclear energy, with a single light bulb containing enough energy to boil all the world's oceans. [...] Yet according to Einstein's theory of general relativity any such energy would gravitate and the experimental evidence from both the expansion of the universe, dark energy and the Casimir effect show any such energy to be exceptionally weak. [...] This discrepancy is known as the cosmological constant problem and it is one of the greatest unsolved mysteries in physics. Many physicists believe that "the vacuum holds the key to a full understanding of nature"
It's your story, so you could said that Zero Point Energy stores a massive amount of power, like Stargate series did.
More information can be found in this answer I post last year:
The problem with antimatter is that you have to expend energy to create it. It might serve as a good energy storage medium, and there are interesting things you can do with animatter that you can't trivially do by other means, but by itself it isn't a source of energy and it couldn't replace fusion (there are potentially similar problems with creating small black holes that produce useful amounts of hawking radiation, but those might perhaps be worked around).
However, imagine if you had a means to construct a non-orientable wormhole. Things you feed through a non-orientable wormhole may come out the other side, but their chirality (or "handedness") will be flipped. Dextro-amino-acids become their levo-equivalents. Southpaws come out as regular boxers. Matter comes out as antimatter.
Suddenly every fleck of matter in the universe is a source of a great deal more energy than you could ever get out of it from fusion alone.
If you don't believe in wormholes and like your power sources to be more dangerous than black holes, consider strangelets. It is possible that massive strangelets are more stable than their smaller versions, and in that case it may be practical to throw a lump of regular matter into a strangelet which will convert it to strange matter and release a generous quantity of gamma rays. You obviously wouldn't want one of these anywhere near your star or planet, and it doesn't give you as much energy as actually annihilating the inflowing matter would, but it would be a pretty effective power source nonetheless.
If you'd prefer something a little safer, you might like Q-balls. No spacetime-warping trickery required, but you may need to live in a universe with supersymmetry and it increasingly looks like we don't. That aside, these are exotic forms of quark matter, related to strangelets. Unlike strangelets, q-balls don't eat up everything and emit gamma rays, and perhaps more importantly from a safety point of view can be charged and so trapped in a suitable electromagnetic apparatus. If you take the right kind of q-ball, and shoot a beam of the right kind of particle at it, the particles will be reflected off with their chirality changed: another source of antimatter.
It is remotely possible that natural q-balls exist and might be harvested, if any were found within practical range of your spacecraft.
Penrose process
By splitting a chunk of matter in two near a black hole in such a way that one piece drops into the black hole and the other escapes it, one can extract its rotational energy.
This has way better energy efficiency than fusion (about 29% of original BH mass can be harvested), possibly more when using charged black holes.
