How do I file 1098-T for state of TN scholarships for dual enrollment courses of a high school student? TT seems to not process dual enrollment 1098-T's properly.

If the box 1 amount is fully covered by the box 5 amount, then just don't enter the 1098-T. The 1098-T is only an informational document. The numbers on it are not required to be entered onto your tax return. 

The ability of the parent of a high school student to claim the education credit is limited.  If these courses are provided by an eligible college, this cost qualifies for the Lifetime Learning Credit (LLC). The school must have policy of granting college credit for that course, already taken, if the student ever enrolls there. In other words, it is a requirement that the course be a college credit course, even if the student isn't currently a college student. It’s not that the student is post-secondary, it’s that the course is post secondary. Books are not a qualifying expense, unless included in the course fee. You must have paid tuition to the college and not the high school in order to claim the expenses on your return.

https://www.taxact.com/support/22177/2023/education-credits-high-school-student-taking-college-classes?hideLayout=False

High school students are not usually eligible for the more generous American Opportunity Credit, unless they are officially enrolled as a degree candidate.  

After answering no to both the degree seeking and credential seeking questions, you will get a screen titled "did you take college level classes in 2024". Answer yes. The fine print says "Note: Answer yes if you took the classes as a high school student".