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This article will help you on how to deal with a moss issue.

https://www.gardeningknowhow.com/ornamental/foliage/moss/killing-moss.htm

It is likely that there is something trailing down the path, and tossing it, looking for insects, and grubs under the moss.

There is a method that I recommend to keep pests off of it. This will not harm the moss. Just slice up some hot peppers and boil them in a few cups of water. When this cools, strain off the peppers and put the water in a spray bottle. Spray all of the moss that you can, and there won't be much that will bother it anymore.

Rototilling, as well as pouring boiling water on the patches will get rid of it. You can also try raising the pH of the soil with dolomitic lime to kill it off. Using all three methods will likely kill most, if not all of it.

This is likely caused by highly compacted soil. It is not allowing water to drain properly, which is causing mosses and algae to grow. You will have to aerate the yard, and reseed with some new grass. This will make it hard for anything but the grass to grow, since they will outcrowd most other plants.

This article will help you: https://www.gardeningknowhow.com/lawn-care/lgen/aerating-your-lawn.htm

Please include a photo, and I will be more than glad to help you with this.

The marble ball is not a good object for moss to adhere to.

You can make a sphere with chicken wire and pack with Sphagnum Moss.
You can then attach the moss. You will need to mist the moss ball periodically.

https://www.gardeningknowhow.com/ornamental/foliage/moss/propagating-moss.htm