No, you do not split the 1098-T between you and your son. Either you claim the 1098-T or you don't claim the 1098-T. Below you will find my explanation of the two scenarios.
I have read through your previous posts and the responses from @Hal_Al. You do not have to split anything. If he is your dependent, then you can claim the education credit on your return.
One thing that I do not see mentioned above, is that your son cannot claim the 1098-T on his return if he is a dependent on your return. The only way you can claim the credit is if he is a dependent on your return.
I am going to give you two scenarios here. One with you claiming your son and claiming the 1098-T on your return.
Scenario 1: The credit is going to be calculated by the amount in Box 1 ($1,695) of the 1098-T and subtracting Box 5 of the 1098-T ($2,740) which leaves a credit of $1,035. This would cause a taxable event unless you applied the cost of books and other eligible educational expenses ($1,393) to the remaining credit which would leave the balance of $1,035 would be considered income except you applied the to that amount of $348 the amount eligible for the education credit. I am not sure how much of a credit you would receive from this amount.
Your son then has to deal with the 1099-Q. The only thing he can claim against the 1099-Q is his room and board which is $6,964. Where there any other expenses he paid other than rent such as utilities? If so, add those to the amount of room and board. Taking the amount on the 1099-Q ($8,304) less the amount of room and board ($6,962) leaves $1,342. Your son would have to report the $1,342 as income.
Scenario 2: Since your education credit is very limited, let your son claim himself, and you do not claim him a dependent. Your son would have his $4,125 of income plus the taxable amount of $1,342 from the 1099-Q, but would also get the credit for the $348 from the 1098-T which would leave him with a taxable amount from the 1099-Q of $992 instead of $1,342. His total income would be $$5,117 and with his standard deduction, he would not pay any taxes. If you continue to claim him, then he will receive a standard deduction for the earned income of $4,125 and pay tax on the $992.
