  Let $\mathbb{F}_q[t]$ denote the ring of polynomials over $\mathbb{F}_q$, the
finite field of $q$ elements. We prove an estimate for fractional parts of
polynomials over $\mathbb{F}_q[t]$ satisfying a certain divisibility condition
analogous to that of intersective polynomials in the case of integers. We then
extend our result to consider linear combinations of such polynomials as well.
