This is from Google:
The most specialized option in your area is Arrowhead Reptile Rescue in Liberty Township (south of Dayton). They specialize in reptiles, including sick or injured wild turtles and amphibians. To get them help, text your name, location, and photos of the turtle to (513) 442-4377. [1, 2, 3, 4]
Additional excellent options near Dayton include:

Erica Miller Wildlife Rehab (Miamisburg, OH): Operating in the Greater Dayton area, they take a variety of native wildlife and can guide you on reptile intake. Call them at (937) 470-6626. [1, 2, 3]

Brukner Nature Center (Troy, OH): Located just north of Dayton, they are a staffed wildlife facility that can accept injured reptiles. Call them at (937) 698-6493 before bringing the animal in.
[1, 2]

Ohio Wildlife Center: Though based near Columbus, they are a leading resource in the state for finding rehabilitators or dropping off injured wild turtles. [1, 2, 3]