1098 T and 1099 Q - Do I include the 1098 T and 1099 Q on my children's tax returns or on my tax return? or on both?

It depends. For 529 plans, there is an “owner” (usually the parent), and a “beneficiary” (usually the student dependent). The "recipient" of the 1099-Q can be either the owner or the beneficiary depending on where the money was sent. When the money goes directly from the Qualified Tuition Plan (QTP) to the school, the student is the "recipient".

The 1099-Q gets reported on the recipient's return. The recipient's name & SSN will be on the 1099-Q.
Even though the 1099-Q is going on the student's return, the 1098-T should go on the parent's return, so you can claim the education credit. You can do this because he is your dependent.

You can and should claim the tuition credit before claiming the 529 plan earnings exclusion. The educational expenses he claims for the 1099-Q should be reduced by the amount of educational expenses you claim for the credit.
But be aware, you can not double dip. You cannot count the same tuition money, for the tuition credit,  that gets him an exclusion from the taxability of the earnings (interest) on the QTP. Since the credit is more generous; use as much of the tuition as is needed for the credit and the rest for the interest exclusion. Another special rule allows you to claim the tuition credit even though it was "his" money that paid the tuition.
In addition, there is another rule that says the 10% penalty is waived if he was unable to cover the withdrawal with educational expenses either because he got scholarships or the expenses were used (by him or the parents) to claim the credits. He'll have to pay tax on the earnings, at his lower tax rate (not yours), but not the penalty.

Total qualified expenses (including room & board) less amounts paid by scholarship less amounts used to claim the Tuition credit equals the amount you can use to claim the earnings exclusion on the 1099-Q. 
Example:
  $10,000 in educational expenses(including room & board)

   -$3000 paid by tax free scholarship

   -$4000 used to claim the American Opportunity credit

 =$3000 Can be used against the 1099-Q (usually on the student’s return)

Box 1 of the 1099-Q is $5000

Box 2 is $600

3000/5000=60% of the earnings are tax free

60%x600= $360

You (or he) have $240 of taxable income (600-360) 

I filed my taxes already. I decided to file my tuition this year for the first time. I used my 1098-T from the university and entered the amount from box 1 ($2512.70). This brought my return up to $3,115, stating that I would be receiving about $2100 in federal credits. I recently received a 1099-Q from my Florida prepaid tuition plan. Do I need to amend my submitted tax return when I get my refund? I do not want to be penalized next year for this mistake. Thank you

I have a couple questions about this  topic also. i hope it is ok to post them here. 

Our family received a 1098-T under my son name and he is in college. We also received a 1099-Q under my name. I am filing income tax for my son (single status) and us (me and my wife as join status).  Next year I will try to have the 529 money send to my son's school instead of our account so the1099-Q will have his name on it and everything will be file on his return.

Here are questions:

1. How do we correctly file these forms on our returns (my son return  and my return) this year?

2. I believe there is a income limitation for claiming the tuition credit and our income is over that so I can put those form on my son return for this year even though 1099Q is under my name and 1098-T is under his name. This way the tuition credit is more advantageous for him instead of us ? 

my 24 yr old son is in medical school. We provided financial support for his room and board for 11 months of last year. He received  Post911 GI bill money for his tuition 1/21-6/21. He had taken out student loans to cover the fall while he waited to see if got another military scholarship. He then commissioned in 9/21, and is now receiving an Army HPSP scholarship for tuition and a taxable stipend,but it was not received until 11/21. Thus he did make more than $4300(stipend), so we cannot claim him as a dependent. The Army not only back paid his tuition for the fall of 21, but also paid his spring 22 tuition at the same time....so his 1098-T shows scholarships/grants for 3 semesters and only Tuition for 2 semesters.We also pulled out the remaining money in his 529 since we had been paying all of his room and board expenses so we received the 1099-Q.  Due to the overage in box 5 or the 1098T should we just use both the Q & T on our taxes even though we know we won't get a tax credit?