What variety is it . Some varieties have long stems on the figs.

Normal fruits of this variety are so how you can see on this picture. There's only ONE branch on the tree that's producing NOW those malformated fruits.

That is very strange. The leaves look like they have rust too.

It's not now but in late autumn when leaf-rusting is a normal phenomenon. This picture served just for showing the variety in question. The phenomenon I presented at the start that's very-very strange never seen: the fruits on the places of the terminal buds.

Mark it and collect cuttings to see if that mutation persists, it looks similar to fasciation.

https://en.wikipedia.org/wiki/Fasciation

It's been marked.
Yes, it is a fasciation. I hope the causation is not any viral or bacterial infection. If the mutation persists we can create a new ornamental fig variety by multiplication in vitro.