One minor misdemeanor will not usually disqualify someone from obtaining custody of a child --- if that is the only hiccup in their background and they otherwise qualify to have custody.  The courts use a "best interest of the child" standard to decide custody matters.  In doing so, they usually look at the whole picture and the whole person to decide what will be best for the child in the long run.  Considering the time frame and the minor nature of the infraction, it should not have a major impact on custody, assuming that all other factors are good.  Other factors would include being able to provide a good home, having a stable job, and being a good parent in general.  If you had an abusive history, then the result would be much different.