Anything we put forward without more info than just the pictures is going to be a guess. The white portion is pretty obviously softer than the rest of the stone, since you can see deeper wear near the edges. The white part is not much softer than the rest though, since it’s barely eroded more than the rest. It might be from a half to a full point softer on the Mohs scale. Or it might even be the same hardness but appears to wear more quickly because it’s more crystalline than the rest.
That being said, it looks a bit like a river worn jade with quartz veins. It also looks like it could be marble. There’s just no telling without more info.