Step 1: Set the context of fossil fuel combustion.
Fossil fuels (coal, petroleum, and natural gas) are burned to produce energy. During this combustion, carbon and nitrogen compounds react with oxygen at very high temperatures, releasing various gases.
Step 2: Check Carbon dioxide (CO2).
Carbon (C) in fossil fuels combines with oxygen (O2) during complete combustion to form carbon dioxide. This is the primary greenhouse gas emitted, so CO2 IS an emission.
Step 3: Check Nitrogen oxide (NOx).
At the extremely high temperatures inside engines and furnaces, atmospheric nitrogen reacts with oxygen to form nitrogen oxides. These are direct combustion by-products, so NOx IS an emission.
Step 4: Check Ozone (O3).
Ozone is not released directly from burning fossil fuels. It forms later in the atmosphere when NOx and volatile organic compounds react in sunlight. It is a secondary pollutant, not a direct emission.
Step 5: Check Hydrogen (H2).
Hydrogen is itself a clean fuel. It does not appear as a by-product when fossil fuels burn. In fact, hydrogen combustion produces only water vapour. So Hydrogen is NOT an emission of fossil fuel burning.
Step 6: Choose the option not emitted.
Since the question asks for the gas NOT emitted due to burning fossil fuels, and Hydrogen is never released during fossil fuel combustion, it is the correct answer.
\[ \boxed{ \text{(C) Hydrogen} } \]