In Ohio the TANF Program is called the Ohio Works First Program

Ohio Works First (OWF) is the financial assistance portion of the state's Temporary Assistance to Needy Families (TANF) program.
This program provides cash benefits to eligible families for up to 36 months.

If you are an Ohio resident you can apply for the OWF program at this local Job and Family Service Office.

OR

You can use the online system in Ohio for the Ohio Works First Program along with healthcare, childcare, food and cash benefits.
https://benefits.ohio.gov/

Each County Job and Family Services agency sets its own policies for hardship and good cause extensions. The emphasis of OWF is self-sufficiency, personal responsibility, and employment. OWF requires adults receiving benefits to work or engage in work related activities, such as educational or training programs. Once you have returned the form to our office, you will be scheduled to call our toll free call center at 1-844-640-6446 to speak to one of our caseworkers, who will determine your eligibility.