So let $\mathbf{F}_q$ be a finite field with $q$ elements where $q=p^m$,

$p$ a prime number and $m\in\mathbf{Z}_{\geq 1}$. Let $f(x,y)\in \mathbf{F}_q[x,y]$

be a smooth non-constant polynomial and let $A:=\mathbf{F}_q[x,y]/(f)$.

Q: Does there exists an integer $N_0$ (which depends on $A$) such that for $N\geq N_0$ one

may always find a prime ideal $P\subseteq A$ such that $A/P\simeq\mathbf{F}_{q^N}$?