Hello everyone?
The lsu purple fig tree cutting that I am growing is only leafy and the roots have not yet come out. How can I save it? Please
help me.  

I would put it back in your growing media, raise the humidity, and lower the lights. Darkness should help the roots come out. 

I would expect those leaves to die off soon.  But don't worry.  Once you get roots, new leaves will follow.  Roots are priority.

I agree about removing the leaves. A plant that small cannot support so many leaves. It would be best to remove all but one leaf. That way the root feeders which should form in the next few weeks should be able to keep it going. 

Keep leaves on, but when they fall off wrap those stems with parafilm. You'll need the energy from those leaves.