Quote from the 6th novel, Chapter 1 Part 8 (Credit for the translation goes to Baka-Tsuki):
All the students in Academy City had a scholarship they could claim, and the money would be automatically banked into their accounts like a salary.
On first glance, it was a system that was worth being envious over, but basically, it could be considered a contract for esper development. The more prestigious the school, or the higher the Level of the esper, the greater the reward. In contrast, the esper would have to take part in more research.
As for ordinary Level 0 school students like Kamijou, the reward they could get was rather limited.
All Espers (even the Lv.0s) should have this scholarship for the Power Curriculum Program, the program to develop Esper-powers.
Not included here are non-students: Skill-Out most likely earns money with crimes, Teachers are paid by the city (although they don't get money for being a member of Anti-Skill), and foreigners (like Frenda) just live in the city and get paid for their jobs.