Which gender has the stuttering genetic strait that can be passed on to their children?

Not known: I am not aware of a sex-linked genetic causality for stuttering, although more men than women stutter. Wikipedia has an accurate entry on stuttering. http://en.wikipedia.org/wiki/stuttering.

Hard to predict: As genetic research of stuttering is only in its infancy it is hard to predict which gender has more chance of transmitting the gene. But as a rule of thump the sex that suffers less tends to be a bigger carrier, but it may or may not hold true in case of stuttering.