The father has legal custody but is now incarsarated for back child support on another child.Can I get temporary emergency custody?

Depends on how long he is going to be in jail. You should have the child now, where is the child. Were there reasons you do not have custody ?

Who are you to the child? Custody should go to the child's closet relative, assuming that person wants the child and can care for the child. How custody is obtained depends on where the child is now and local laws.