Renan's answer highlights important facts on radiation penetration through ice (limited for gamma, functionally non-existent for beta electrons & alpha nuclei), and the greater plausibility of chemoautotrophic organisms. However, I can add a little on potential photon-centric mechanisms in case that is of interest.
The main important piece of information is understanding that life fundamentally lives on chemical energy gradients. Get some way to acquire spare energy that can transform complex molecules and you can probably hack together some form of self-replication from those molecules.
On Earth we find life building off photosynthesis (whereby an incoming photon has its energy captured by the chlorophyll molecule, and then clever chemistry leads to that energy being redirected to do microbiological work building up complex molecules elsewhere in the cell), or chemotrophic life that leaves near (eg.) ocean volcanoes and "eats" the exotic sulphur compounds, which are highly reactive with carbon-ish molecules and thus can be used to do microbiological work.
In theory, the photons of gamma radiation could be captured and used in the same way as visible light is in photosynthesis, you just need a chlorophyll-esque molecule that is tuned to the energy of some appropriate photons (captures the photon, promoting the chlorophyll to a higher energy vibration or ionisation that can be utilised in further organic reactions). The considerable difficulty here is that gamma radiation generally imparts enough energy to ionise/break bonds in organic material, destroying the lifeform.
Possible Solution for Gamma-feeders: You either need an organism that is made of sturdier stuff than hydrocarbons, or invent a system where your organisms generate some shallow stabilised dendritic tunnels in the ganymedean ice, then sit at a deeper level (recall that gamma penetrates ice poorly) and pump a photosynthetic liquid through the tunnels, reabsorbing the energised compounds that come back, but not directly exposing themselves to the gamma radiation. The details are tricky --- in real-life you need to chemically utilise chlorophyll's absorbed photon in a few hundred nanoseconds or else the chlorophyll converts the energy to useless heat --- but doable.
Possible Solution for Beta-feeders: Beta radiation can easily ionise organics, which in principle could be used as an energy source for organic reaction, although the chemical pathway would be somewhat different. However, beta radiation is more destructive to molecules than gamma radiation (electrons carry more energy than photons), giving us far thornier versions of the destruction problem from earlier. Furthermore, any location that has beta exposure would have to be on the surface of the ice, meaning direct exposure to gamma and alpha radiation. I cannot imagine a lifeform living sensibly in such conditions without a completely novel chemical makeup to resist radiation damage.
Possible Solution for Alpha-feeders: None. Alpha radiation is helium nuclei getting flung around. Sure, they carry lots of energy, but trying to use them for organic reactions is like trying to catch a bowling ball with a cobweb.