  We propose a supersymmetric quantum field theory with exotic symmetry related
to fracton phases. We use superfield formalism and write down the action of a
supersymmetric version of the $\varphi$ theory in 3+1 dimensions. It contains a
large number of ground states due to the fermionic higher pole subsystem
symmetry. Its residual entropy is proportional to the area instead of the
volume. This theory has a self-duality similar to that of the $\varphi$ theory.
We also write down the action of a supersymmetric version of a tensor gauge
theory, and discuss BPS fractons.
