If life ever existed on Mars, and was of a form that could leave fossilised impressions, there is every reason to suppose that fossils exist on Mars. As yet, there is no evidence at all that life has ever existed on the Red Planet. (A key ingredient for life, water, does exist in the form of ice.)
In 1996, a team of scientists claimed to have found evidence of fossilised bacteria in a fragment of Martian meteorite, but the claim was later rejected. Although NASA’s Perseverance rover, now on Mars, is designed to look for chemical traces of life, it is not equipped to find fossilised remains. That will require a sample return mission.