If the child did not live in your home more than half the year, you generally can't claim him as a dependent.
I think @Bsch4477 assumed you were the foster parent. If the child is placed with a foster parent for more than half the nights of the year, and the placement is via the state or a state-approved agency, then the foster parent can claim the child as a dependent. Because the child can be claimed by the foster parent, no one else can claim them child, even if the foster parent will not actually claim him. This can't be waived or shared, even if both people agree. If you are not the foster parent and the child did not live in your home more than half the nights of the year, you can't claim him as a qualifying child dependent.
If the child moved around, and did not spend more than half the nights of the year (183 or more nights) in any one home, then things get tricky. No one can claim him as a qualifying child dependent for the $2000 child tax credit. Someone might be able to claim him as a qualifying relative or "other" dependent for a $500 credit, but only if
a. that person paid more than half his total financial support
b. or, that person provided more than 10% of his financial support, and every one else who provided more than 10% of this support signs a multiple support agreement agreeing that you can claim the child and they won't.
As a practical matter, if no one else claims the child as a dependent, you might not get caught if you claim him. But that doesn't make it right.
