Secondary terms for first moments of Selmer groups of twists of elliptic curves over global function fields

Let $E$ be a non-isotrivial elliptic curve over a global function field ${\mathbb{F}}_q(t)$ of characteristic coprime to $2$ and $3$. Under some explicit conditions, we determine the secondary terms for the first moments of prime Selmer groups of cyclic prime twist families of $E$ over ${\mathbb{F}}_q(t)$.