Existence of Connected Non-T1 Scattered Space

Theorem
There exists at least one example of a connected topological space which is not a $T_1$ (Fréchet) space, which is also a scattered space.

Proof
Let $T$ be a divisor space.

From Divisor Space is Connected, $T$ is a connected space.

From Divisor Space is not $T_1$, $T$ is not a $T_1$ (Fréchet) space.

From Divisor Space is Scattered, $T$ is a scattered space.

Hence the result.