Is there any way for an Internal Medicine resident, who is interested in Endocrinology, subspecialize within Endocrinology to go into Reproductive Medicine? I know that OB/GYN residents have the option of going into REI fellowship, but is there anything equivalent when going down the path of Endocrinology?
For female fertility, not really. You can do simple stuff - all of us work up PCOS for example. Some might do some very very simple infertility treatment in that specific situation - try a cycle of Clomid for the PCOS patient - but most of us would refer to REI. Certainly there's no way to get training in IVF.
For male fertility, still not really, but andrology is a lot less formalized of a field than REI. You may be able to carve a little bit of a niche there, but even still you're unable to do any procedures like sperm extraction, so better off leaving it to the Urologists.