  We introduce a unital associative algebra ${\mathcal{SV}ir\!}_{q,k}$, having
$q$ and $k$ as complex parameters, generated by the elements $K^\pm_m$ ($\pm
m\geq 0$), $T_m$ ($m\in \mathbb{Z}$), and $G^\pm_m$ ($m\in \mathbb{Z}+{1\over
2}$ in the Neveu-Schwarz sector, $m\in \mathbb{Z}$ in the Ramond sector),
satisfying relations which are at most quartic. Calculations of some low-lying
Kac determinants are made, providing us with a conjecture for the factorization
property of the Kac determinants. The analysis of the screening operators gives
a supporting evidence for our conjecture. It is shown that by taking the limit
$q\rightarrow 1$ of ${\mathcal{SV}ir\!}_{q,k}$ we recover the ordinary
${\mathcal N}=2$ superconformal algebra. We also give a nontrivial Heisenberg
representation of the algebra ${\mathcal{SV}ir\!}_{q,k}$, making a twist of the
$U(1)$ boson in the Wakimoto representation of the quantum affine algebra
$U_q(\widehat{\mathfrak{sl}}_2)$, which naturally follows from the construction
of ${\mathcal{SV}ir\!}_{q,k}$ by gluing the deformed $Y$-algebras of Gaiotto
and Rap$\check{\mathrm{c}}$\'{a}k.
