When the Fig Tree is dormant you can prune any diseased or damaged branches.
A Fig Tree is generally productive with or without pruning.
It is usually only essential during the early years of growth.
When the tree is well established, avoid heavy winter pruning since this can effect the next crop.
It is better to prune after you have harvested the fig crop.
If you have a late ripening cultivator you should prune half the branches in summer and then prune the remainder of the branches the following summer.
https://www.gardeningknowhow.com/edible/fruits/figs/pruning-fig-trees.htm
https://www.gardeningknowhow.com/edible/fruits/figs/potted-fig-tree-pruning.htm