I haven't seen that pattern called anything in pure breeds that I can think of... I would call it barnyard mix, cuckoo cross or whatever cutesie name you can come up with.
To me barred and cuckoo are the same thing just different terms depending on which breed it's being used in. But I also am no expert.Do you think it is part cuckoo? It seems more barred than penciled to me, and that's what I would guess. But I'm no expert obviously. I love this pattern.
The new pic does look much more like the following description!Here is a newer picture of her.
Looks like juvenile feathering for the partridge pattern. While it may not be pure for partridge per say, it is close to the partridge phenotype.
I don’t see any barring on her.