The fact that they are still a Full-Time student means that they can earn over $4,700 and you can still claim them as a dependent. However, if they pay for more than half of their own support, then you would not be able to claim them.
As the non-custodial parent of a 19 year old, you may not gain any tax benefits from claiming your son as you are not eligible for the EIC and since they are 19, they would only be eligible for the $500 Non-Refundable Other Dependent Credit. Since your income is already below the filing threshold, you would not have any tax liability and would not be eligible for the Other Dependent Credit for that reason.
You may however, be able to claim the refundable portion of the American Opportunity Credit which is $1,000. You would NOT be able to claim the full credit as part of it is considered non-refundable. See the answer by Champ Hal Al for a detailed explanation on how to maximize your credit and minimize their scholarship income
qualifying child
Tax Info for NonCustodial Parent
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