You can still claim him if he meets the criteria. The fact that he had income on his own does not by itself disqualify him from being claimed as a dependent.
You never claim your dependent's earned income on your return. Your dependent must file his/her own return, if their income exceeds the filing threshold amounts.
Someone being claimed as a dependent must file his or her own federal tax return if they had earned (W-2) income over $12,000; or self-employed (1099-MISC) net income over $400; or unearned income (interest, dividends, capital gains) over $1,050. (2018 numbers) (State filing thresholds may be different.)
Even if their income is below these thresholds, they'd still have to file a return in order to get a refund of any withheld taxes.
IMPORTANT: If your dependent does file a tax return, be sure they indicate on it that someone else can claim them as a dependent.
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