  We study the algebraic geometry of twisted Higgs bundles of cyclic type along
complex curves. These objects, which generalize ordinary cyclic Higgs bundles,
can be identified with representations of a cyclic quiver in a twisted category
of coherent sheaves. Referring to the Hitchin fibration, we produce a
fibre-wise geometric description of the locus of such representations within
the ambient twisted Higgs moduli space. When the genus is 0, we produce a
concrete geometric identification of the moduli space as a vector bundle over
an associated (twisted) A-type quiver variety; we count the number of points at
which the cyclic moduli space intersects a Hitchin fibre; and we describe
explicitly certain $\mathbb{C}^\times$-flows into the nilpotent cone. We also
extend this description to moduli of certain twisted cyclic quivers whose rank
vector has components larger than 1. We show that, for certain choices of
underlying bundle, such moduli spaces decompose as a product of cyclic quiver
varieties in which each node is a line bundle.
