Illegitimate students in Singapore are not allowed to take part-time jobs.

However, those who have legal work permits in Singapore can take part-time jobs in schools (even if they go to private schools).

These steps are

1. Find a job in Singapore and apply for a work permit.

2. Look for the school slowly while going to work.

3. Apply for the school and wait for admission.

4. Go to school while going to work until graduation.

But it's hard to find a job and a school, because you are a foreigner.