You didn't specify whether your child is currently developing in your mates body or if you're still planning to conceive. You just stated that you're taking Regaine and you're worried about the safety of your child.
Are you female and having the child yourself?
Need more information.
Either way, actually, the advice given here will be the same: Please discuss this with your doctor. You need someone who will be responsible for the advice given to you.
I can comment based on experience that a male taking finasteride can conceive safely (inseminate). The reason for this is because it takes several weeks before the male genetalia of the potentially male fetus begins to develop. This is the susceptible time period where finasteride (not regaine) might cause problems, and it only happened in studies where mass amounts of it were injected directly into the fetus. You won't have that kind of volume in your semen, and finasteride will be long gone by the time 24 hours rolls around, let alone several weeks.
I would however for my own peace of mind, avoid continually "finishing inside of her" through the pregnancy. There's no reason to continue injecting small amounts of finasteride into your wife while she is pregnant. I would wear a condom and keep the pills away from her skin. Again, have your doctor give you the final word, as we are not qualified to give medical advice like this here.
-G-