we are owners of a construction company in Ohio. must we pay owners Prevailing wages
Generally speaking, it appears from your question that the project is indeed a prevailing wage project. If that is the case, then you, as the employer of a company working on that project, are obligated to follow Ohio's prevailing wage statute.
This means you (the employer) must, (a) pay prevailing wage rates for your employees, as determined by the law (and the Public Authority in charge of the project) for your county, (b) generate and submit certified payroll reports to the Public Authority's prevailing wage coordinator, (c) provide your employees with wage notification forms and submit copies to the prevailing wage coordinator, and (d) strictly comply with all other requirements of Ohio's prevailing wage law (Ohio Revised Code Chapter 4115).