  $W(a,b)$ and $W(a,b;\bar{a},\bar{b})$ algebras are deformations of
${\mathfrak{bms}_3}$ and ${\mathfrak{bms}_4}$ algebra respectively. We present
an $\mathcal{N}=2$ supersymmetric extension of $W(a,b)$ and
$W(a,b;\bar{a},\bar{b})$ algebra in presence of $R-$symmetry generators that
rotate the two supercharges. For $W(a,b)$ our construction includes most
generic central extensions of the algebra. In particular we find that
$\mathcal{N}=2$ ${\mathfrak{bms}_3}$ algebra admits a new central extension
that has so far not been reported in the literature. For
$W(a,b;\bar{a},\bar{b})$, we find that an infinite $U(1)_V \times U(1)_A$
extension of the algebra is not possible with linear and quadratic structure
constants for generic values of the deformation parameters. This implies a
similar constraint for $U(1)_V \times U(1)_A$ extension of $\mathcal{N}=2$
${\mathfrak{bms}_4}$ algebra.
