Literature on Quadratic Residues in Polynomial Quotient ring

Question

I have a literature-question. Given a field $\mathbb{F}$, finite or infinite, and an element $f$ in the polynomial ring $\mathbb{F}[t]$. I am searching for results of any kind about quadratic residues in the quotient ring $\mathbb{F}[t]/\langle f \rangle$, if they exist. Can anyone recommend a good book/paper on that topic?

Thanks a lot!