In the ADE-classification, the items labeled $A3$ include the following:
$\mathbb{Z}/4$
the dicyclic group
$Dic_1 \simeq \mathbb{Z}/4$
as simple Lie groups: the special unitary group in 4 complex dimensions
as a Dynkin diagram/Dynkin quiver:
The A3 Dynkin diagram coincides with the D3 diagram, hence with the result of removing one node from the D4 diagram. In the classification of simple Lie groups this coincidence reflects the exceptional isomorphism between SU(4) and Spin(6):
ADE classification and McKay correspondence