Fossil Models are simply models of the skeletons of dinosaurs. They are listed as mobs because they are coded as entities. The dinosaurs that currently have fossil models are: allosaurus, ankylosaurus, brachiosaurus, ceratosaurus, compsognathus, deinonychus, gallimimus, liopleurodon, mosasuar, plesiosaur, pteranodon, spinosaurus, stegosaurus, triceratops, and tyrannosaurus.
To create a fossil model, right-click to place a Bio-Fossils on the ground. A model of a random infant mob will spawn. To make them "grow," right-click them with bones. The hitbox of these models, no matter what size, is a small area near the feet or arms, which can be hard to find. Right-clicking this hitbox with an open hand will rotate the model. Punching the hitbox breaks the model, returning to the player the bio-fossil and bones.
Tar fossil models are basically darker versions of the models and are only Cenozoic creatures. They are made when a tar fossil is placed instead of a Bio-Fossil.