After you unlock Slate's Barn in Rusty's Retirement and unlock the ability to keep farm animals, fossils will begin to appear sporadically on the farm.
Rust is even harder than you think
Collecting them is important because you need some to buy extra farm animals to make fertilizer, which will reduce the time it takes for crops to grow and allow you to unlock more of each farm.
After a while it may seem like fossils stop spawning, but that is not the case.
You can get more fossils on your farm in Rusty's Retirement by adding more animals to your farm.
