The fossil fuels are no longer fossils, there is no DNA or anything like that in them. They call them fossil fuels because they are basically derived from large quantities of prehistoric carbon based life that died and then was compressed over many millenniums inside soil, until it reduced to other forms of carbon, namely oil and coal.
Most fossil fuel is actually derived from prehistoric plant life, algae, and fungus anyways, so you wouldn’t likely find bones or anything. For example, the reason the middle east is the #1 location of oil is that hundreds of millions of years ago it was home to a vast ocean, covered in algae and plant life. That plant life died and collected at the bottom of the ocean, eventually became covered in sediment, and more sediment, etc, etc….. Fast forward to today, it’s been converted to oil.