The short answer to this question is: maybe, depending on your relationship with your step child. If you have legally adopted your step child, under the law, you are considered as the child's legal parent. See O.C.G.A. §19-8-6(a)(2) and O.C.G.A. §19-8-6(a)(1). As a legal parent of your step child, (via step parent adoption) you have the same rights to child custody as the child's other legal parent (your current or soon to be ex-spouse). This is so, because upon adoption of a child, the legal relationship between the child and the biological parent who consents to the adoption is terminated. Thus, the child is no longer viewed as the legal child of the consenting parent, but as the legal child of the adopting parent. Please note, that as with any other child custody contest between parents, the judge presiding over the matter will determine the child's custodial arrangement with the best interests of the child in mind, and will only make a custody award that suites the child's best interests.
However, if you are a step parent who has not yet legally adopted your step child via the process of step parent adoption, you are not viewed, legally, as the legal parent of your step-child. Thus, under normal circumstances, a court will likely not award custody to you as opposed to the child's legal and biological parent. If you are considering step parent adoption, there are two ways in which a child may be adopted by his or her step parent. If the child's other biological parent is no longer living, the child may be adopted by the spouse of his or her living parent only if that parent consents in writing to the adoption. O.C.G.A. §19-8-6(a)(2). On the other hand, if both the child's biological parents are still living, a child may be adopted by his or her step parent only if the other parent voluntarily surrenders his or her parental rights in writing and the other parent consents in writing to the adoption. O.C.G.A. §19-8-6(a)(1).