They were common in Ohio, I remember talking about these with my dad (many years ago). He was born in 1926 had clay marbles as a child on a farm in Ohio.
I gotta agree with Loco here, clay marbles were quite common in the U.S. in the early 1900s and probably earlier. I have several hundred non-dug ones and some dug ones. Capa, yours is a large one, most of my plain clay ones are smaller although I have a bunch of glazed clay ones that size. I always like digging up the early marbles.
Hard to tell the exact size from the pic, sometimes the object looks bigger if it projects toward the camera lens while the ruler is back. It looks like it is an inch or under in size. If it were a clay shooter marble, then one would expect it to be normally about 7/8 of an inch but 1 inch is still in the parameters of these marble sizes. Your normal ones were more like 5/8 in diameter, but remember that these were handmade and could be any size that they wanted.Some clay balls were much larger for other games that were played in the 19th century. Marbles are pretty common finds anywhere kids played, but usually are found on the surface of a plowed field or if you are sifting a site...unless you are using a marble detector