You have come across some very oil rich shale. Unfortunately, I don’t see anything that looks fossil to me.
What I see is that oil rich shale has allot of mineral precipitation going on, causing the different patterns and colors, some of which you can rub off (thin layers of precipitation).
The white areas that seem to branch again look like mineral precipitation lines that follow weak spots and microscopic cracks in the shale. The oilyness (if that’s a word) probably helps spread it. This is similar to how dendritic mineral growth occurs. The dendritic growth looks like little trees and stuff forming on the rock. Yours is not quite the same, as it has more of the branching that you see. If you google “dendritic mineral growth” you can see how this type of precipitation occurs.