An exemption is the deduction ($4050) that your get for claiming someone as a dependent. If you do not meet the rules for claiming someone as a dependent, you do not get the $4050 exemption from taxation.
No, you cannot claim a child's exemption if he lived with the other parent. The
custodial parent has first priority on claiming the children on her taxes;
regardless of the amount of support provided by the non-custodial parent. The
non-custodial parent can only claim the child's exemption (claim the child as a dependent) if the custodial
parent gives permission (on form 8332) or if it's spelled out in a pre 2009
divorce decree.
