We introduce a unital associative algebra \({{\mathcal{S}\mathcal{V}ir\!}_{q,k} }\) , having q and k as complex parameters, generated by the elements \(K^{\pm }_m\) ( \(\pm m\ge 0\) ), \(T_m\) ( \(m\in \mathbb {Z}\) ), 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 \({{\mathcal{S}\mathcal{V}ir\!}_{q,k} }\) we recover the ordinary \({{\mathcal {N}}}=2\) superconformal algebra. We also give a nontrivial Heisenberg representation of the algebra \({{\mathcal{S}\mathcal{V}ir\!}_{q,k} }\) , 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 \({{\mathcal{S}\mathcal{V}ir\!}_{q,k} }\) by gluing the deformed Y-algebras of Gaiotto and Rap \(\check{\textrm{c}}\) ák.
