If the calendar term for that semester was 8/17/20 - 12/18/20, that is considered parts of 5 months ( not4 mths), which is one of the requirements for a "Qualifying Child" dependent.
However, he needs to have supplied less than half his financial support, for the entire year (not just the school term).
There are two types of dependents, "Qualifying Children"(QC) and standard ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit, student status, a relationship test and residence test.
A child of a taxpayer can still be a “Qualifying Child” (QC) dependent, regardless of his/her income, if:
- He is under age 19, or under 24 if a full time student for at least 5 months of the year, or is totally & permanently disabled
- He did not provide more than 1/2 his own support. Scholarships are excluded from the support calculation
- He lived with the parent (including temporary absences such as away at school) for more than half the year
So, it doesn't matter how much he earned. What matters is how much he spent on support. Money he put into savings does not count as support he spent on him self.
The support value of the home, provided by the parent, is the fair market rental value of the home plus utilities & other expenses divided by the number of occupants.
The IRS has a worksheet that can be used to help with the support calculation. See: http://apps.irs.gov/app/vita/content/globalmedia/teacher/worksheet_for_determining_support_4012.pdf
If he does not meet the QC, rules, then he must have had less than $4300 of income, for all of 2020, to be a Qualifying Relative dependent, instead. The support test, for a QC, is only that the child didn't provide more than half his own support. The support test for a Qualifying Relative is that the taxpayer provided more than half the relative's support.
