The understanding we have of how energy is gained from nuclear fission/fusion reactions is based on the prinicle of mass-energy being conserved. When nucleuses of certain combinations of protons and neutrons combine or split into nucleuses with differnt combinations, the total mass of the same amount of protons and neutrons changes. This is usually modelled as a difference in nuclear binding energy, were the nuclear binding energy is the energy released when a nucleus is formed. This is equal to the mass differential between the sum of the protons and the neutrons.
https://www.energy.gov/science/doe-explainsnuclear-fusion-reactions
https://en.wikipedia.org/wiki/Nuclear_binding_energy
When an object is moved away from the centre of the earth, it requries energy to do so, this energy does not change the qualities of the object apart from its position. It does not heat up, emit different frequency radation, and when stationary at the start and end of this process, has the same kinetic enegy macroscopically.
https://en.wikipedia.org/wiki/Gravitational_energy
I propose a test where atomic nuclei are combined or split with a fusion or fission reaction on the surface of earth. With the energy released measured. Then that same process is repeated at a much higher altitude, where energy has to be put into the nuclei (modelled as them gaining gravitational potential energy) in order for them to change posititions.
If when these nuceli undergo fusion or fission at a different altititude, the energy released from the reaction is the same as when the reaction occurs on the surface of earth, then energy will have been lost, as the total amount of energy that can be gained from the new nuceli returning to the surface of earth is lower, due to the fact that the mass of the nuclei is lower.
If the energy that can be gained from the movement of the nuceli back to earth is lower, then mass-energy will have been destroyed, violating the conservation of mass-energy principle.
To summarise, energy would be used up to move nuceli further away from the earth, currently modelled as a conversion to gravitational potential energy, energy would be released from a fission or fusion reaction at this altitutde due to the change in mass of the nuceli, the total gravitational potential energy that could be recovered from moving these nuclei back to earth would be lower than the total amount of graviational potential energy that could be gained by their ascent away from earth. This would be due to a difference in total mass, this would violate the mass-energy principle in theory.
As far as I'm aware there haven't been any experiments that have tested this. It would be interesting to find out the results of such an experiment, as quantum mechanics, general relativity, and newtonian physics are known to not be in allignment anyway. Nuclear physics using non-relativistic quantumn mechanics, and gravitational potential energy being calculated using newtonian or relativistic physics.