When is the best time yo prune my dwarf Yaupon Holly?
I have a Prince Edward Holly and I went to a reputable garden center and the owner told me how to treat it and its doing well . So try that.
Around here (zone 9) it can be sheared almost any time. It is often grown as a green hedge, without concern for the fruit.
If you want the see the fruit, then prune it before it after the fruit show so it has time to grow more flower buds for next year's crop. I would avoid pruning it when any new growth response would get hit by freezing temperatures.