  We introduce two classes of right quaternionic Hilbert spaces in the context
of slice polyregular functions, generalizing the so-called slice and full
hyperholomorphic Bargmann spaces. Their basic properties are discussed, the
explicit formulas of their reproducing kernels are given and associated
Segal--Bargmann transforms are also introduced and studied. The spectral
description as special subspaces of $L^2$-eigenspaces of a second order
differential operator involving the slice derivative is investigated.
