Paraphysis
As paraphyses you have long called sterile organs between the reproductive organs of mosses and fungi are.
The sac fungi ( ascomycetes ) they are between the Asci . Together with the asci, they form the hymenium (fruit layer) of the fungus.
The multicellular sap hairs that stand between the male ( Antheridium ) and female ( Archegonium ) reproductive organs in the deciduous mosses are also called "paraphyses".