If you work off the books can you still file for your child

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Working "off the books" is self-employment, or being in business for yourself. You have to report all the income as business income and pay tax on it. Self-employment income or business income is considered earned income. Since you are reporting the income, you are eligible for any tax benefits based on having a child that require earned income, including the child tax credit and the earned income credit, if you meet the other requirements for those credits.