I'd give the barred bird some time but if you are sure you are right on the parentage and the father was not barred but the mother was, then due to genetics it can't be anything other than a cockerel, unless it has some weird genetic mutation. This is due to it being a sex linked trait:
Chickens have Z and W chromosomes, Males have ZZ and females have ZW
Barring is a sex linked trait, bound to the Z chromosome[which means barring can only be on a Z chromosome and not on a W one] which is why male pure barred birds are lighter in color than females, they have two copies of the barring gene, while females can only ever have one, because they only have one Z chromosome.
Now if you breed an unbarred male to a barred female, you only get males with a single copy of the barring gene, and females with none.
The barred female genetically decides the sex, and she always contributes a barred Z to males[males can not take the W, or they'd be female], and an unbarred W to females [females need to have the W from the mother, as the father only has two Zs].Since the father has two unbarred Z's, one of those is the other half of what the chicks get, so the males are always single-barred and the females always unbarred.
It doesn't work the other way around, because a pure barred male has two barred Zs and would thus always give a barred Z to his offspring, resulting in all single barred chicks.
