If you are saying dad gets SSI, then there are no additional benefits for the dependent children. SSI pays a certain amount to disabled individuals, depnding on household income, but does not pay benefits for the dependent children.
So, I assume you are saying dad had been approved for Social Security disability and the kids are getting no money. That is likely for one of 2 reasons: Dad is getting workers' comp benefits, which reduces benefits that would be paid to the "auxilliary" beneficiaries first, like children; or because when dad worked and paid taxes, he did not earn enough reported income that taxes were paid on to get benefits for the children. SS Disability (not SSI) is based on the disabled person working long enough and earning enouhg - and paying taxes on what wa searned. So jobs where cash was paid and no taxes were taken and paid to the government, or where earnings were low (part time work, temporary fulltime work with gaps iof unemployment, or just low wages) means thatn the dependents are not eligible for any benefits.
Talk to SSA and they will answer the questions for you.
I hope this information helps. Good luck to you!
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