No, your child's right to Supplemental Security Income, SSI, will not be impacted if you claim them as a dependent on your return. Neither will their right to Medicaid.
Xmasbaby0, above, is correct, your child's SSI benefits should not be reported on your return and if that is their only income, they do not need to file as the IRS will already have that information from the Social Security Administration.
You child may also be a qualifying person for you to claim the Earned Income Credit and if you are a single parent, may qualify you to claim Head of Household.
This is an IRS list of resources for tax benefits and credits for those living with disabilities. Not everything there will apply to your family but it may point you to additional information that will be helpful. IRS Living and Working with Disabilities
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