If you are working privately for someone and are self-employed, then you would need to keep records of your income and expenses and file as a self-employed individual. This means, you will need to make quarterly payments to the IRS. Your quarterly payments will consist of your ordinary tax rate and an additional 15.3% for your Social Security and Medicare taxes.
You can make your payments online through the EFTPS.
Since you are also working part time as an employee, you can adjust your W4 to have more taxes withheld. You can the TurboTax W4 estimator to adjust the withholdings on your wages to cover your self-employment income depending on how much you make working for someone vs your private pay job.
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