  We introduce an elliptic algebra $U_{q,p}(\hat{sl_2})$ with $p=q^{2r} (r\in
\R_{>0})$ and present its free boson representation at generic level $k$. We
show that this algebra governs a structure of the space of states in the
$k-$fusion RSOS model specified by a pair of positive integers $(r,k)$, or
equivalently a $q-$deformation of the coset conformal field theory
$SU(2)_k\times SU(2)_{r-k-2}/SU(2)_{r-2}$. Extending the work by Lukyanov and
Pugai corresponding to the case $k=1$, we gives a full set of screening
operators for $k>1$. The algebra $U_{q,p}(\hat{sl_2})$ has two interesting
degeneration limits, $p\to 0$ and $p\to 1$. The former limit yields the quantum
affine algebra $U_{q}(\hat{sl_2})$ whereas the latter yields the algebra ${\cal
A}_{\hbar,\eta}(\hat{sl_2})$, the scaling limit of the elliptic algebra ${\cal
A}_{q,p}(\hat{sl_2})$. Using this correspondence, we also obtain the highest
component of two types of vertex operators which can be regarded as
$q-$deformations of the primary fields in the coset conformal field theory.
