My son filed for 2018 and was rejected because his father claimed him. He is 20 and is not a student. Does he need to file?

If your son's 2018 income is above $12,00, he must file a return.  If his income is $12,000 or below, he doesn't have to file unless he wants to get back any taxes withheld. 

If he does decide to file, he should mark that someone else can claim him as a dependent

You can indicate that you were claimed as a dependent by following these steps--

First, to get back into your return after printing or e-filing, please follow these steps:

1. In TurboTax Online, sign into your account.
2. Select Tax Home in the left menu.
3. Scroll down to Your tax returns & documents.
4. Select 2018, and then select Add a State (you're not actually adding a state, this just gets you into the right menu).
5. Once you're in your return, you can navigate around as usual.

To indicate that you are a dependent of someone else:

1. Click My info in the black bar at the left of your screen.
2. Click on Edit next to your name. 
3. In section #3, mark the box that Someone else can claim me on their tax return. 
   
4. Then mark the circle And this person will claim me on their 2016 return.
5. Continue with the rest of the return.
6. To re-file the return, click File (in the black bar on the left)
   

He must file Federal if he had self-employment income of more than $400.
State filing requirements may be different.

"He is 20 and is not a student"
His Father cannot claim him if his 2018 income was more than $4,150.