You can claim your 20 year old full-time college student as your dependent. The 1098T goes on YOUR tax return.
MY DEPENDENT HAD A JOB
If your dependent has a W-2 for his after-school job, summer job, etc. you do not include the information on your own return. You can still claim your child as a dependent on your own return. He/she can file his own return for a refund of some of his withheld wages (he won’t get back anything for Social Security or Medicare), but MUST indicate on it that he can be claimed as a dependent on someone else’s return. (Supervise this closely or prepare it for him!)
If your dependent’s earnings were over $400 and were reported on a 1099Misc then he must file a return and pay self-employment tax for Social Security and Medicare. You may want to use this version of TT for that: