Is there a specialty that

Deals with the both the male reproductive system and the females? And if something is wrong with these systems?
Reproductive endocrinology. I think most male issues are dealt with by a urologist, though. A urologist does the work up for male hormonal or structural problems (would do biopsies, u/s, etc to diagnose).

My guess would be fertility clinics.

when my husband i had our fertility work-up done, a urologist did his preliminary check, my obgyn did some of mine but referred both of us to an endocrinologist, and finally we had extensive genetic screening.

undoubtedly, endocrinology is the answer the specialty of the male & female reproductive system, btw great field to get into...good luck...ciao~

endocrinology isn't going to give you a lot of opportunity to, umm, handle these "systems," if you get my drift and if i get yours. you could definitely go to a general urology floor-- many genders have urological surgery, some that might surprise you.