My son is 20 but cannot be claimed as a dependent because he makes too much. I share Marketplace with him. Do I check box that says I will have a dependent filing taxes?

No, if he isn't your dependent, you won't check that box.  

 Both you and your son need to enter a copy of the Form 1095-A that you received on your tax returns. TurboTax will ask you questions about if the policy was shared with someone and how to allocate the costs and credit. Follow the instructions below.

1. Login to TurboTax and select Federal and Deductions & Credits
2. Scroll down to Medical and select Show More
3. Select Start/Revisit next to Affordable Care Act (Form 1095-A)
4. Answer yes, I received Form 1095-A
5. Enter the information and select Continue
6. Select I shared this policy with another taxpayer who’s not on my taxes and Continue
7. On the next screen you will enter the SSN for your son and the start and end months that you shared the policy with your son
8. You will also choose the percentages of the amounts you want to claim on your tax return.  Both percentages should add up to 100%
9. TurboTax will calculate the information that should be on your return based on your answers.

The percentages that you should enter for your premium, your SLCSP, and your advance payment should be an amount that you and the person you share it with agree on. It could be 50/50, 100/0, or another amount. Make sure you are in agreement and that the percentages on both tax returns add up to 100% together.

To enter Form 1095-A refer to the TurboTax Help article Where do I enter my 1095-A?