A student who is underage for getting driving licence goes to school by driving bike then he does a job and he got a job because of his study and will his income become halal or haram because he goes to study by driving a bike and it was illegal for him to drive underage as he broke traffic rules , he studied by going through breaking traffic rules so do his study and income be halal or not?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

Riding a bike without a license has no effect on the academic degree or on the job.

As long as he has obtained the certificate rightfully and worked in a permissible job while performing the required work in his job as due, then his earnings are lawful and there is no problem in it.

Allah Knows best.