The world of disability benefits can be a very confusing place. There are many different programs that a person can apply for, and it is important to know the difference between all of them. A particularly touchy subject is government benefits for children. Particularly if a child is born with a severe medical condition or cognitive difficulties, parents may not be able to support them independently where their medical costs are concerned. This is why there are governmental programs to help with supporting these children. However, according to the Social Security Administration, if you are applying for benefits on behalf of your disabled child, you will apply to SSI, not SSD.
Children are not eligible for SSD in the vast majority of circumstances, given that SSD is awarded in the case of disability and work credits. As disabled children under the age of 18 are unlikely to have any sort of work history, this disqualifies them for SSD automatically. There are some special circumstances where the legal guardian has SSD and thus the child may be entitled to some form of support through SSD as a result, but these circumstances are rare.
A disabled child is eligible for SSI under special requirements applied to minors until the child reaches the age of majority. Then the child will need to apply for SSI under the same requirements as other adults.
Disabled children are also eligible for Medicaid, though the rules for this are going to vary wildly between states. Medicaid is often dependent on family income, but children with disabilities do get special consideration here as well, particularly if the cost of their medical care would be prohibitive to the family.