It depends on the bandgap of your solar panel's semiconductor

Solar panels work by absorbing a photon and using it to "boost" an electron in the silicon lattice. Once boosted, the electron is free to wander around the lattice and do work until it gives up its energy and returns to the lattice (through a process called hole-electron recombination). Thus, an electrical current is created.

Photons are of course quantized, so a single photon can only eject a single electron. Einstein showed this through his explanation of the photoelectric effect. In it he found that the photon must have a minimum energy or no electron would be ejected, in other words, a photon's energy was quantized. This was actually the birth of quantum mechanics.

Getting back to your gamma-ray solar panel, yes, it is feasible to engineer a panel that can absorb gamma rays, but it will not increase the number of electrons available (i.e. the current). In theory, however, it could increase the energy of the electron when it's ejected (i.e. the voltage).

Since power is P = VI, you could, theoretically, increase the power by absorbing gamma rays, but it's not that simple.

Modern photovoltaic cells are only about 20% efficient. Most of the photons falling on them are unable to eject an electron and are thus converted to heat. This isn't necessarily related to the photon's energy, either, it has to do with how the solar panel is engineered. So in the end, the amount of power you can generate with your solar panel is directly related to its efficiency, not the energy of the photons it absorbs.

All of it falls down to what's called the "band-gap energy." This is a measure of how easy it is in your semiconductor to eject an electron, and it has direct implications on the power and voltage that your semiconductor operates at.

There are multiple kinds of band gaps, but the one you care about is the optical bandgap. For pure silicon this is about 1 electron volt. For our purposes, 1eV is equal to 1V, so a single silicon wafer can generate 1 volt of electricity. The amount of electrons is going to be related to the surface area of the cell, and thus so is the current. In order to get higher voltage, you string the panels together in series. To get more current, you would string the panels together in parallel.

For pure silicon, we can calculate the optimal photon wavelength required to eject an electron, and it turns out to be around 1 micrometer, which is not even in the visible spectrum; it's near-infrared!

But one of the useful properties of certain semiconductors is that its bandgap energy can be changed through doping. In silicon, this is very difficult to do, but in other semiconductors such as Gallium Arsenide and Indium Phosphate, it's relatively straightforward.

This band-gap engineering is how engineers control the color of LEDs. Namely, by changing the band-gap energy to be roughly the photon energy (and thus the color of the photon).

For your gamma-ray semiconductor to work, you would need to engineer your solar panels to support the gamma-ray energy photons available. However, this would be in direct conflict with attempting to make your panel absorb other wavelengths, such as visible light.

It's not really a significant energy source. If you measure wattage carried by photons that pass through a particular volume of space, gamma rays are not very significant. Visible and infrared light are the wavelength where you find the most wattage. That ratio is basically the same whether you're close to a sun or not. In deep space, far from any sun, you'll get very little energy from any form of light.

It's different if you're near a neutron star or active black hole which emit more energy in the short wavelengths. Though they still have more energy in x-rays than gamma rays.

But, your gamma ray absorbing panels would make excellent radiation shields.

One of the problems with gamma rays is that they go through everything. Gama rays don't interact with things very often, which means they will likely go through solar panels without being absorbed. If these fictional gamma panels are effective at absorbing gamma rays, then they may be more valuable as shielding than as power collection.

Real world gamma ray shielding involves massive blocks of lead, concrete, water, or whatever. The only way to block gamma rays is to put enough stuff in front of it that it gets absorbed eventually. If you had a lighter, thinner mechanism to block gamma rays that might be a big deal. Especially if your ships frequent high radiation environments or if their enemies utilize gamma-ray lasers.