If a rock contains fossils, then it is not a meteorite. Fossils occur in Earth rocks because there is life on Earth. Thus far, we do not have evidence of life on any of the places where meteorites come from, so if a rock contains fossils, then it is an Earth rock. If we ever find a meteorite that contain fossil life forms, that would be a big deal, but the burden of proof would be very heavy.
The author is a lunar geochemist who has never taken a course in paleontology, so I apologize if any of these objects is not actually a fossil. Three of the photos were sent to me by persons who thought the rocks might be meteorites. The one in the upper right is of a rock I found myself while searching for meteorites in Antarctica (at a place unofficially known as “meteorite moraine”). I showed it to a real paleontologist who thought it might be a species of palm. It does seem to have a bark.
A weak connection between meteorites and fossils (Antarctica used to be a warm place).
Coalsack Bluff, Transantarctic Mountains, as seen from “meteorite moraine.” Wikipedia: “The discovery of Lystrosaurus fossils at Coalsack Bluff in the Transantarctic Mountains by Edwin H. Colbert and his team in 1969–70 helped support the hypothesis of plate tectonics and strengthen the theory, since Lystrosaurus had already been found in the lower Triassic of southern Africa as well as in India and China.”