  $\mathcal{N}=1$ superconformal minimal models are the first series of unitary
conformal field theories (CFTs) extending beyond Virasoro algebra. Using coset
constructions, we characterize CFTs in $\mathcal{N}=1$ superconformal minimal
models using combinations of a parafermion theory, an Ising theory and a free
boson theory. Supercurrent operators in the original theory also becomes sums
of operators from each constituent theory. If we take our $\mathcal{N}=1$
superconformal theories as the neutral part of the edge theory of a fractional
quantum Hall state, we present a systematic way of calculating its ground state
wavefunction using free field methods. Each ground state wavefunction is known
previously as a sum of polynomials with distinct clustering behaviours. Based
on our decomposition, we find explicit expressions for each summand polynomial.
A brief generalization to $S_3$ minimal models using coset construction is also
included.
