If I am a part-time student who turned 24 last year, and whose part-time job was not enough to cover more than half of my living expenses, can I still be claimed?

[ep_marie10]

As a part-time worker, I made more than $4,000 in 2019, however, it was not enough to support myself; therefore, I still lived/was financially supported by my parents.

[VolvoGirl]

Sorry if you turned 24 and made more than $4,200  you can not be claimed by anyone.   They can not claim you anymore.  

[Hal_Al]

No.

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.

Since your turned 24, you cannot be a QC and the $4200 income limit now governs.