Sister is the relationship between female siblings of the same father and mother. For most animals like ourselves we get an assortment of each of our parents DNA to make ours. 50% of our DNA is identical to each of our parents. Siblings to ourselves will get a different assortment so 50% of my DNA is identical to my sister on average.
Bees are different, drones have only one copy of the DNA. So workers with the same drone father get identical copies from him (100%). Since they get half the mother (queen) DNA (50%) they are more closely related (75%) than human sisters and are sometimes referred to as super sisters.
But the queen mates with several drones, so bees from different drones share no father DNA (0%) only the queens DNA (50%) so on average will have 25% identical DNA. They are half sisters, much the same as for humans with different fathers.
Several authors refer to these relationships as sub-families in a hive, one closely related subfamily per drone that the queen mated with. You can sometimes recognise workers which are alike and those not alike in a hive, it's particularly striking if one parent had a DNA abnormality such as a different eye colour.
Sub sister isn't a term that I recall being used in the books I've seen. Is it a synonym for bee half sisters? You would have to ask whoever was using it. Addition: found at least one US reference using it as a synonym for half sister, i.e. the workers in a hive are all either super sisters or sub sisters.