Fibered $p$-biset functor structure of the fibered Burnside rings

We determine the composition factors of the $A$-fibered Burnside functor $k{B}^A$ for $p$-groups over a field $k$ of characteristic $q$ with $q\mathrm{\ne }p$ and cyclic fiber group $A$. We also show that, in this case, $k{B}^A$ is uniserial.