The amount on my son's 1098-T received is $8187 and the payments received for qualified tuition is $7199. I only spent $298 in books and other expenses. What do I do

I assume  you are saying box 1 of the 1098-T is $7199 and box 5 is $8187.

There is a tax “loophole” available. The student reports all his scholarship, up to the amount needed to claim the American opportunity credit, as income on his return. That way, the parents  (or himself, if he is not a dependent) can claim the tuition credit on their return. They can do this because that much tuition was no longer paid by "tax free" scholarship.  You cannot do this if the school’s billing statement specifically shows the scholarships being applied to tuition or if the conditions of the grant are that it be used to pay for qualified expenses*.

Using your numbers as  an example: Student has $8187 in box 5 of the 1098-T and $7199 in box 1 and $298 of book expenses  ($7497 total expenses). At first glance he has $690 of taxable income and nobody can claim the American opportunity credit. But if he reports $4690 as income on his return, the parents can claim $4000 of qualified expenses on their return.

You can both use the 1098-T to enter the expenses. If you claim the tuition credit, you do need to report that you got one (the TurboTax interview will handle this) Your son should use the 1098-T because it makes entering scholarship income go smoother.

You can use a work around in TurboTax (TT). Here's how I would do it. Enter the 1098-T, on your return, but only enter $4000 in box 1. No other numbers. You only enter the 1098-T to get TurboTax to check the proper box on form 8863. Lying to TurboTax to get it to do what you want does not constitute lying to the IRS. The 1098-T is only an informational document. The exact numbers on it are not required to be entered onto your tax return. 

On your son's return, enter only $4690 in box 5. 

*This is not some sinister scheme. From the 2019 form 1040 instructions (pg 95): “You may be able to increase an education credit if the student chooses to include all or part of a Pell grant or certain other scholarships or fellowships in income. For more information, see Pub. 970, the instructions for Form 1040, line 18c, and IRS.gov/EdCredit.  Page 16 of PUB 970 (2019) actually has examples of how to do the “loop hole”.