Vaginal skin fold

If by under you mean between your vaginal entrance and anus, it is unusual.

If it is in front(belly side) where your inner and outer lips meet at the top, you just discovered your clitoris.

It is not my clitoris as I discovered that years ago and that has feeling when touched unlike this peice of skin.

The elongated penis shaped extra skin I have is inside my Labia Minora - so attached to the area above my Vaginal entrance but below my Urethra <---- closer to the Urethra hole.
It looks like it is a cover for my Urethra but I know that is not the case.
In another forum someone suggested it might be my Hyman.... Yeah Nah - I am not young and that went years ago (two decades to be precise!!!)

I have a healthy sex life and this peice of skin has never gotten in the way not that I ever knew it was there.

I in my 30's and was checking out my stitches with a mirrir - (Had a mole removed on inside of leg) and found this little thing

I'm still a little freaked and am wondering if I should go to the doctor for them to have a look but want to know as much information as possible so I don't look stupid.

Regarding hymens,
A friend once told me she had something that sounds similar to what you have, only on the bottom of her introitus. Hers was a skin tag.