I have a fig cutting that I got in July was growing very well outside, I brought it in the middle of Oct. and has been growing well under lights, up until 2-3 weeks ago. Puts new leafs on the size of a quarter or half dollar than falls off. It has done it about 5-6 times, but the stem is still growing. It is a white fig, and came from a friends father in a town near Rome Italy.

What am I doing wrong?
To much water, not enough water?

Since it looks like you have new growth I'd say just not enough light.  Just like you have to transition figs into full sun when initially under grow lights the leaves that grew under full sun and matured under full sun light intensity would probably take longer to drop off when brought inside but the new leaves are trying to grow under lower light levels.  I've had figs start fruiting inside before but that was in full sun in a window with southern exposure.  I also have three humidifiers going 24/7 just to get to 40% humidity here in the New England winter.  Figs do need to go dormant to ensure good fruit production also, so you might just want to put it outside in a protected area to go dormant.

My house is between 40and 45% humidity, my other figs under the same light are not losing there leaves and are putting on new growth.  I though I read that the first year you should let fig cutting go dormant, to keep them going for better root growth. I do not know, this is my first year at starting cutting. All ways open for suggestion and willing to learn. Thanks for the come back and suggestion.