The Skill Brother
Fossilized Drake, Bird, Fish and Dino are more common when digging with the Skill Brother. In Pokemon Shield, Drake and Fish fossils are abundantly more common. In Sword, Bird and Dino fossils are.
If you haven't already, an NPC in the Stow-On-Side Pokecenter will give you 2 fossilized Drakes or Birds, depending on your version. (Shield has Drakes, and Sword has Birds.)