e minor

my fingers seem to be to short to play this cord without some part of my hand touching other strings. unless I reach over the top.

Which fingers are you using? For instance, I use my middle & ring fingers just as one would to form the Emaj, with the index finger up and off of the 'g' string to get the E minor. Using my index and middle finger to form an E minor is a rare occurence. Another possible factor; is your palm resting on the back of the neck? For most open chords, I only use my thumb- anywhere from the tip to the joint depending on the wrist angle- which acts as a very low-friction pivot point for switching between chords. I also tend to use only my thumb on the back of the neck on barre chords and chord fragments, unless the manner in which they're being used warrants that good ol' baseball bat grip.

I don't know if any of that helps, but no two hands are exactly alike so you may have to experiment with your grip and which fingers to arrive at a comfortable solution.

If you turn the guitar where you can see where you are putting your finger, you are impeding your reach.. If you are playing on classical guitar you are playing on a wide neck.. Or you missed something in your basic lessons..
I could not find the lesson you would need to look, but I did find several you tube videos
good luck..