What finish is on it now? What material is the doorstep made of? Pictures?

It's actually door threshold made of wood.

If that is is there in the center of that pic it has been painted already. I would prep well and paint again.

I would remove it, and clean and sand it well, and paint it with a high quality paint. It looks like it gets a lot of foot traffic, and probably should not have ever been painted. You could also replace it with another one, since they are not all that expensive, and then not put any paint on it, so it will stay nice longer.