I paid half my tuition since I work part time and my parents another portion, who should claim education expenses? I’m listed as a dependent already under my parents.

Dependents cannot get education credits.   If you can be claimed as a dependent on your parents' return, they are the ones who can enter the education credit.

As the other reply said, the education credit follows your dependency. 

Furthermore, the education credit is 60% non-refundable, so your parents are more likely to get a bigger credit than you would. 

Furthermore, a full time unmarried student, under age 24, even if you don't qualify as a dependent, is only eligible for the refundable portion of the American Opportunity Credit if he supports himself by working. You cannot be supporting yourself on parental support, 529 plans or student loans & grants.

It is usually best if the parent claims that credit.