The biosphere is the outer part of the Earth with waters and air which is inhabited by living beings, the largest ecosystem.
The fossilized organisms do not form part of the biosphere. So carbon is fixed in the Earth. When we burn coal or petrol (for energy), we add carbon to the biosphere. Some ecological laypeople believe this can be neutralized by planting trees; well, trees fix carbon temporarily outside of the atmosphere, however it stays within the circulation of the biosphere.