  We study $\mathrm{SL}_2(\mathbb{F})$-character varieties of knots over
algebraically closed fields $\mathbb{F}$. We give a sufficient condition in
terms of the double branched cover of a $2$-bridge knot (or, equivalently, of
its Alexander polynomial) on the characteristic of $\mathbb{F}$, an odd prime,
for the $\mathrm{SL}_2(\mathbb{F})$-character variety to present ramification
phenomena. Finally we provide several explicit computations of character
varieties to illustrate the result, exhibiting also other types of
ramification.
