does my wife's boyfriend have grounds to get custody of there kid if she gets back with me?

Unfortunitly, you question is very vague and there is little to go on to provide a response.  The short answer is, it depends.  In Ohio there is no preference given to the mother or the father of the child when one, the other, or both are seeking custody.  In determining issues of custody the Court uses the "best interest of the child" test.  Factors the Court uses to determine the "best interest of the child" are: (a) The wishes of the child's parents regarding the child's care; (b) If the court has interviewed the child in chambers pursuant to division (B) of this section regarding the child's wishes and concerns as to the allocation of parental rights and responsibilities concerning the child, the wishes and concerns of the child, as expressed to the court; (c) The child's interaction and interrelationship with the child's parents, siblings, and any other person who may significantly affect the child's best interest; (d) The child's adjustment to the child's home, school, and community; (e) The mental and physical health of all persons involved in the situation; (f) The parent more likely to honor and facilitate court-approved parenting time rights or visitation and companionship rights; (g) Whether either parent has failed to make all child support payments, including all arrearages, that are required of that parent pursuant to a child support order under which that parent is an obligor; (h) Whether either parent or any member of the household of either parent has a history of child abuse; (i) Whether the residential parent or one of the parents subject to a shared parenting decree has continuously and willfully denied the other parent's right to parenting time in accordance with an order of the court; (j) Whether either parent has established a residence, or is planning to establish a residence, outside this state.   For more information visit us at www.Sylkatis-Law.com & www.LorainDivorceAttorney.com