Adult dependent

If he is a full time student and under the age of 24 in 2024, then you should be able to claim him as a dependent under the Qualifying Child rules if he meets all the requirements.

To be a Qualifying Child -

1. The child must be your son, daughter, stepchild, foster child, brother, sister, half brother, half sister, stepbrother, stepsister, or a descendant of any of them.
2. The child must be (a) under age 19 at the end of the year, (b) under age 24 at the end of the year and a full-time student or (c) any age and permanently and totally disabled.
3. The child must have lived with you for more than half of the year. Temporary absences while away at college are considered living with you.
4. The child must not have provided more than half of his or her own support for the year.
5. If the child meets the rules to be a qualifying child of more than one person, you must be the person entitled to claim the child as a qualifying child.
6. The child must be a U.S. citizen or U.S., Canada or Mexico resident for some portion of the year.
7. The child must be younger than you unless disabled.

• Relationship test. The child must be your son, daughter, stepchild, foster child, brother, sister, stepbrother, stepsister, half brother, half sister, or a descendant of any of these, such as your grandchild, niece, or nephew
• Residency test. The child must have lived with you for more than half of the year. Time away at school still counts as living with you.
• Age test. The child must be:
  • Under age 19 at the end of the year and younger than you (or your spouse if MFJ), or
  • Under age 24 at the end of the year, a full-time student for some part of each of any five calendar months during the year, and younger than you (or your spouse if MFJ), or
  • Permanently and totally disabled at any time during the year,
    regardless of age.
• Support test. The child cannot have provided over half of his own support during the year.

In your case, it sounds like there are only two areas to be concerned about:

1. The age test, but you already mentioned he's a full time student, so you should be good there.
2. The support test. If he's only working part time, and he's living with you, it sounds like he's not providing more than half of his own support, but that's what you'd want to be sure of before claiming him.

While your son is an adult, he is considered a qualifying child and will be able to be claimed as a dependent on your return.  In his situation, because he is a full-time student, under the age of 24, he lives with you and even though he works part-time, he probably does not provide more than half of their own support.

Here is a link to a TurboTax Article with the rules for Claiming Dependent on Taxes. 

Rules for Claiming Dependents on Taxes   https://turbotax.intuit.com/tax-tips/family/rules-for-claiming-a-dependent-on-your-tax-return/L8LODbx94#GoTo-What-is-a-dependent-