Child support will not stop and any tax you would have to pay for a summer job would be very minimal. If you are allowed to work at 15, give the employer your SSN.
Unless your parent's child support order contains a really unusual provision related to your own income, your own income will not affect the legal obligations to support you. You may have to be creative in your job search, and don't overlook volunteer work. When approached sincerely and diligently, it can lead to paying work.
Best wishes for a favorable outcome, and please remember to designate a best answer.
This answer is offered as a public service for general information only and may not be relied upon as legal advice.