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when you say "my child" I assume you are the father? If so, you file a custody action with the court. To do this you file a petition for custody. As a natural parent, if the other parent is in jail, it should be fairly simple.
If you are a grand parent, it should also be fairly simple, so long as the other parent (father?) does not object.
If you are not a relative,then it is harder, but if you are acting in place of the parent, you too could file for custody as you are in loco parentis (in the place of a parent).
If you don't want or need custody, but just need a "guardianship" from the Mother, than she could give you guardianship / power of attorney papers....
http://www.romingerlegal.com/custody/index.php (Custody Tips)
1. What kind of response are you looking for?
2. And am I correct in noting that your questions was, and I quote:
"how do i get gaurdenship of my child if mother is in jail"
Please correct your question if you intended a different question, and I will try to assist.