  It is shown that the deformed Heisenberg algebra involving the reflection
operator R (R-deformed Heisenberg algebra) has finite-dimensional
representations which are equivalent to representations of paragrassmann
algebra with a special differentiation operator. Guon-like form of the algebra,
related to the generalized statistics, is found. Some applications of revealed
representations of the R-deformed Heisenberg algebra are discussed in the
context of OSp(2|2) supersymmetry. It is shown that these representations can
be employed for realizing (2+1)-dimensional supersymmetry. They give also a
possibility to construct a universal spinor set of linear differential
equations describing either fractional spin fields (anyons) or ordinary integer
and half-integer spin fields in 2+1 dimensions.
