The physicist Lord Kelvin, born William Thomson, was a world expert upon thermodynamics. He boldly set out to calculate how old the Earth must be. Given the available facts about melting points, heat conduction and transfer, and the experiments to determine the rate at which heat was traveling through the outer layers of the Earth's crust, he concluded that the figure was between ten and a hundred million years, most probably forty million.
This was far more than Ussher's Biblical estimate of six thousand, but far less than the geologists and biologists had concluded from the fact that high mountaintops bore signs of being made at the bottom of the sea.
Subsequent work showed that Kelvin could hardly be blamed for his underestimate, about a hundred times too small, because physics did not then know about radioactivity. To put it another way, the energy that provides geothermal power, drives the Earth's electromagnetic field, supplies tectonic drift, and powers volcanoes and earthquakes, is the energy of slightly unstable atomic nuclei, like uranium, thorium, and the radioactive isotope of potassium. There might be exactly one radioactive isotope produced by solar activity, namely Carbon-14, or 14C. It is produced from stable nitrogen, 14N, in the outer atmosphere, by radiation. Some of that is cosmic radiation, but some might be from the solar wind.
Uranium, thorium, and indeed all the chemical elements whose nuclei have greater mass than that of iron are the product of ferociously high temperatures, much hotter than the Sun's core, because unlike hydrogen, helium, lithium, carbon and so on, when their nuclei are split, the pieces have less mass than the original nucleus. Energy, or mass, has to be added to the pieces to make them combine. They must all have been present already when the Sun's fusion process ignited, and must be the remnants of an exploded superstar, a nova or supernova, or even perhaps something closer in time to the Big Bang.
It follows that if we classify nuclear fission as the use of fossil fuel, it is a fossil older than this planet. And if geothermal resources are not fossil, neither is nuclear.