Apartments For Rent Putnam County . 105 s little river ct, putnam county, ga 31024. How much does it cost to rent an apartment in putnam county? 904908 Putnam Ave, Zanesville, OH 43701 Apartments Zanesville, OH from www.apartments.com Find your next putnam county apartment. Available for june 1, 2022. Some apartments for rent in putnam county might offer rent specials.