For my 1098-T form, my box 1 is not the amount of money that I paid to the school. It was the amount of money that a county paid to the school that organized a cohort.

Box 1 of Form 1098-T reflects the amount that was paid to the school for Qualified Expenses and Tuition. (Usually this is the amount billed by the school). If you then received a scholarship, grant or any incentive, it should be reflected on Box-5. If these amount don't look correct to you, you should contact the institution that issued the 1098-T for a corrected form. 

You should probably treat the discount as assistance.  After entering the the 1098-T, the TurboTax interview will eventually ask if you received any scholarships or assistance not shown on the 1098-T.  You should enter the discount there. 

That said. Be advised that the 1098-T is only an informational document. The numbers on it are not required to be entered onto your tax return. However receipt of a 1098-T frequently means you are either eligible for a tuition credit or possibly your student has taxable scholarship income. 

If you claim the tuition credit, you do need to report that you got one or that you qualify for an exception (the TurboTax interview will handle this)

You claim the tuition credit, or report scholarship income, based on your own financial records, not the 1098-T. In the 1098-T screen, click on the link "What if this is not what I paid the school" underneath box 1. You will then be able to enter the actual amounts paid. You will also reach a screen that allows you to adjust the scholarship amount for "amounts not awarded for 2024 expenses".

Or if you find it easier, just change the numbers in boxes 1& 5 to what your records show. The 1098-T that you enter in TT is not sent to the IRS.