Alan Cameron, in "The House of Anastasius", pages 261-262, argues that
"On this reconstruction Paul had only daughters, three of them. Yet Priscian credits him with sons, so it has usually been inferred. A more careful reading of the relevant passage does not confirm this deduction. At lines 290-94 Priscian praises Paul before evoking in 295 the piety of Anastasius, piety
qua fratris natos animo complecteris aequo,
non patrui tantum, sed patris more colendo,
indole quos nutris dignos et stirpe parentum?
Hypatii vestri referam fortissima facta ...
On the face of it, the 'frater' of 296 might be thought to be Paul. Yet the only one of the 'fratris natos' singled out for individual mention, Hypatius, was unquestionably not a son of Paul. Furthermore, which nephews of Anastasius can a panegyrist writing (as Priscian probably was) in 503 have had in mind but Hypatius, Pompeius and Probus, cons~ in turn for 500, 501 and 502 (Hypatius and probably Pompeius too had both commanded armies as well)? And Hypatius and Pompeius at least are expressly stated to have been sons of Secundinus.
There is no direct evidence for Probus' father, and the one text which mentions all three together, Hypatius, Pompeius et Probus genere consobrini, divique Anastasii nepotes (Marcellinus, Chron. s.a. 532), does not seem to me (pace Stein) necessarily to imply (though it certainly does not exclude the possibility) that all three had the same father. What does seem to me to tilt the balance of probability in favour of this (the usual) conclusion is Priscian's phrase jratris natos'. Had Probus been Paul's son, then it would have been both accurate and tactful, nor would it have made any difference to the metre, for Priscian to have written jratrum natos', to cover Paul as well as Secundinus. He wrote jratris' because all of Anastasius' distinguished nephews were the sons of the same <brother'. It is difficult to believe that an experienced panegyrist would have been so careless as to risk quite unnecessary offense by writing jratris' if he had really been meaning to evoke the sons of two imperial brothers. Secundinus is not actually named because, being only a brother-in-law, he was not him- self (unlike his sons) of the blood royal, nor quite so important a person as Paul-or indeed his own sons, as illustrated by his late consulship. If Paul had had any sons who survived to maturity, we may be sure that they would have received honours comparable to those showered so generously on Secundinus' sons. The fact that none is on record suggests of itself that there were no such sons."
See: https://www.geni.com/documents/view?doc_id=6000000194679552871