Step 1: Evaluate each statement.
\[
\begin{aligned}
I. &\text{True} &&\text{Polygenic inheritance involves cumulative action of multiple genes.}
II. &\text{False} &&\text{Turner syndrome has karyotype }45,X\;(\text{AA}+XO),\text{ not AA+XXY.}
III. &\text{True} &&\text{Dystrophin gene is the longest known human gene.}
IV. &\text{False} &&\text{Chromosome 21 contains the fewest genes, not the highest number.}
\end{aligned}
\]
Step 2: Identify the correct statements.
\[
\boxed{\text{I and III}}
\]
Step 3: Choose the correct option.
Hence,
\[
\boxed{(C)}
\]
is the correct answer.