  In this paper, when the order of $\theta$ is even, we prove that there exists
no central difference sets in $A_2(m,\theta)$ and establish some non-existence
results of central partial difference sets in $A_p(m,\theta)$ with $p>2$. When
the order of $\theta$ is odd, we construct central difference sets in
$A_2(m,\theta)$. Furthermore, we give some reduced linking systems of
difference sets in $A_2(m,\theta)$ by using the difference sets we constructed.
In the case $p>2$, we construct Latin square type central partial difference
sets in $A_p(m,\theta)$ by a similar method.
