Geologist here.

That is core from a diamond drill hole.

There are a number of possibilities as to why it is there, depending on the particulars of your site. Perhaps there has been some mineral activity in your area and some of the core got dumped on site. Perhaps some core got dumped on site from an other area in a batch of dry fill.

Perhaps it was from construction activity, such as the setting of explosives for blasting, although that would be unusual as diamond drilling is much more expensive than percussive drilling, but sometimes the rock is hard enough to justify the expense. Hard to ID the rock (lighting, small grain size, and potato) but it looks as it might be an arkosic sandstone, a meta-basalt or a fine grained intrusive (the overwhelming majority of Ohio is sedimentary, but there are some metamorphic/igneous rocks in the SE), so it might make sense in view of the diamond vs percussive drill options. Perhaps there is a recent road cut or construction site nearby? Or then again you could check if there has been any mining activity in your area.

As to age: definitely 20th to 21st century for technological reasons, but probably much younger because core weathers (and surprisingly fast at that). Your core is relatively devoid of any weathering patina whatsoever, on that basis I'd say it was drilled in the last 20 years, tops.

EDIT: typos

PS: They actually do make passable rolling pins if the diameter is right (say HQ for instance) and the rock isn't brittle or porous. I've used some odd bits of core to that very end on an occasional basis in the field.

I'd say its more likely the trash from a drilling hole for explosive mining, making it no more than two hundred years old. Depending on where in Ohio you are from there is likely an abandoned quarry nearby or upstream.

Looks like this was already answered but in the future I would also recommend /r/whatisthisthing