Apply for Singapore citizenship

You have a companion card and your child has a student card.

In principle, you are not eligible to apply for PR (not RP), and your child is not eligible to apply for PR until he finds a job and holds an SP or EP license.

As far as you and your children are concerned, as the subject of application, you must hold a work permit, not a companion permit. Without a work permit, you can't apply for PR, and you are not qualified. Your child is not eligible to apply until he graduates from a polytechnic or university and finds a job and holds an SP or EP license.

The next step after getting PR is to apply for citizenship, which is the fastest and fastest. I think your child should not apply for citizenship until he is 25 years old (according to the current situation, but the policy may change after more than ten years). As far as you and your children are concerned, there is no doubt that your children are more likely to obtain citizenship. I don't think it's easy for you to get a PR or a citizen unless you change to a work permit. It is basically impossible to get PR by children. Only citizens can apply for permanent residency for their parents. When your child gets citizenship, you will be over 40. Singapore needs new immigrants who can create value for society instead of enjoying the welfare of the elderly. So it is basically difficult to get PR or even citizenship through your children. If you want to get PR and citizens by yourself, you need to find a job locally, and the company will apply for a work permit above SP level for you before you are eligible to apply. However, the current work permit situation is not very good. College degree or above, working experience in related industries may be easier. It depends on your own situation. Do your best. If you can't get a work permit, you might as well concentrate on taking care of the children.