Okay, so I have a planet that gets from its star a solar flux of 1360 W/m^2. The catch? As the star is powered by matter-antimatter reactions, it's predominantly, if not entirely, gamma rays. There is carbon-based life on the surface and deep underground, with the life from the surface being resilient, if not outright immune, to the radiation it gets. The question is: What series of chemical reactions would be the most efficient at converting gamma rays into useful cellular potential energy?
Melanized fungi manage the trick of radiosynthesis, to the point where their attenuation of gamma radiation is such that they're being considered (as in the linked paper) for biological spacecraft shielding.
Specifically, Cladosporium sphaerospermum is a relatively commonplace fungus that manages the trick. So it wouldn't be "photosynthetic life", but it fits the bill.
That said, if your planet has an atmosphere (and it needs to, in order to allow metabolic pathways to operate), and has oxygen, then precious few gamma rays are going to reach the surface. The planet's atmosphere would be warmed by the solar flux, but not lit.
The photosynthesis process doesn't change — cell resiliency and water do
Photosynthesis is merely the process of converting electromagnetic radiation into sugar. Plants favor the blue-green spectrum of visible light because it packs a lot of energy and abundantly passes through everything from the Van Allen radiation belts to the atmosphere to reach the plant.
I wouldn't be surprised if a study on the matter proved radio waves (which are just a lower energy electromagnetic radiation) are converted just fine by plants, but like a gentle breeze against a parked car, there isn't enough energy to do anything. Consequently, the number being very likely a nearly-impossible-to-detect value compared to the bristling energy of visible light, it's ignored.
Likewise, I suspect plants would convert gamma radiation (remember, EM...) just fine — except they can't do it fast enough (were it allowed through to the plant in bulk) before the radiation damaged cell structures in the plant break down (you know, burn up... put a plant in a microwave and you'll kind get what I mean) or the water in the plant vaporizes (...put a plant in a microwave...).
The problem isn't photosynthesis, it works fine and you can find descriptions of how it works all over the Internet
The first problem is cell resiliency.
I frankly have no idea how to describe what would have to happen to plant cell structures to harden them against hard radiation. I do know that as you consider it, you need to keep the word "cancer" written on a post-it right in front of your keyboard.
The second problem is water, which boils in a microwave, which is lower-energy EM radiation than gamma rays.
Even if you hardened a plant's cell structure to handle the radiation damage, the real problem might be water. Water boils (and then vaporizes) very easily in much lower radiation than gamma rays. You either need to seriously pressurize the water or mix it with something like anti-freeze on steroids (which protects against high heat, too) to keep it from boiling away. In short, think about how your car's radiator works and apply that 10,000-fold to your plants. I suspect the believability of your plants will suffer so long as water is the liquid-basis of life on your planet.
I wonder if any of this is actually important? I've read stories that stank because the author was so focused on producing what they thought was incredibly accurate science (that they didn't really understand themselves) that they ended up telling a bad story.
And here's a bit of reality coming from someone who was a micro-publisher for 10 years: If you tell a good story, the vast majority of readers won't care about the scientific specifics. If you tell a bad story, it won't matter how accurate you were with the scientific specifics. If a substantial number of people read fiction because they were interested principally in the scientific specifics, they'd spend most of their time reading technical and scientific journals instead — and in fact, that's actually what they do.