Let me start with what continental drift is. It is the movement of continents on the earth's surface. Which way they move depends on the plate tectonics that they're next to -- divergent, convergent or transform plates). In California you're next to the big San Andreas Fault, which makes California move (or drift) away from the rest of the USA.

To study the continental drift of California, we use satellites and GPS to measure how much it moves every year. But how about the fossils Fossils are organisms, usually animals or plants, that have died and been buried for a long time. So deep underground, the fossils will exist there no matter if the land is moving due to continental drift. The continents will drift whether or not there are fossils so we can say that the fossils will not influence continental drift. But we can use fossils to track how the continents have moved. Let's fast forward 50 million years when California has drifted away from the USA. If there is a plant that only grows in California and Nevada, we will only find fossils of this plant in California and Nevada. We can then trace back that California used to be attached next to Nevada because of the where we've found the plant fossil.

Fossils do not influence continental drift. Fossils on different continents that were once together can let us know that continental drift once occurred, but the fossils were just along for the ride.