My childs father (never maried but is on the birth certificate). If he filed for custody first who has leagal rights? He has a criminal past.

It is not a question of who filed for custody first, but rather who is in the better position to care for the child's needs.  Both parents start on an equal footing and then the court will consider factors, such as who has been the primary caregiver for the child in the past and who is best situated to care for the child in the future. All of the factors used to determine custody are spelled out in Virginia Code section 20-124.3:  § 20-124.3. Best interests of the child; visitation. In determining best interests of a child for purposes of determining custody or visitation arrangements including any pendente lite orders pursuant to § 20-103, the court shall consider the following: 1. The age and physical and mental condition of the child, giving due consideration to the child's changing developmental needs; 2. The age and physical and mental condition of each parent; 3. The relationship existing between each parent and each child, giving due consideration to the positive involvement with the child's life, the ability to accurately assess and meet the emotional, intellectual and physical needs of the child; 4. The needs of the child, giving due consideration to other important relationships of the child, including but not limited to siblings, peers and extended family members; 5. The role that each parent has played and will play in the future, in the upbringing and care of the child; 6. The propensity of each parent to actively support the child's contact and relationship with the other parent, including whether a parent has unreasonably denied the other parent access to or visitation with the child; 7. The relative willingness and demonstrated ability of each parent to maintain a close and continuing relationship with the child, and the ability of each parent to cooperate in and resolve disputes regarding matters affecting the child; 8. The reasonable preference of the child, if the court deems the child to be of reasonable intelligence, understanding, age and experience to express such a preference; 9. Any history of family abuse as that term is defined in § 16.1-228 or sexual abuse. If the court finds such a history, the court may disregard the factors in subdivision 6; and 10. Such other factors as the court deems necessary and proper to the determination. The judge shall communicate to the parties the basis of the decision either orally or in writing. This answer is given in accordance with the laws of Virginia and may not be applicable in any other state.  It should not be construed as legal advice, as that would require a more thorough analysis of all of the facts involved in a specific case.