On question if im supporting someone else like children what should i put since im not going to claim my children this year?

[Anita01]

If you are the custodial parent, meaning the parent with whom the children lived the most during the year, you are the only parent who is entitled to the Earned Income credit, the child care credit, and head of Household using these children.  If the other parent is not the custodial parent, you can allow them to claim the children, but the only things they can receive is a small deduction and the child tax credit.  So, you should answer the questions correctly.

If you are two unmarried parents living with children that are both of yours what I just said does not apply.  In this case, only one of you an claim anything at all related to the children.  The one not claiming the children should not have them on their return at all, so say No if that's you.