a by-product we show that specialization procedure can be also applied to the extended Jordanian twist deformations. Also the underlying covariant quantum space, together with its real form, is introduced in the $q$-analog as well as specialized version. Such $\kappa(\tau)$-Minkowski spacetime with fixed value of parameter $\kappa$ is an universal envelope of solvable Lie algebra without $h$-adic topology. This version has been already considered by some authors, e.g. in the context of spectral triples [@Andrea; @SitDur; @Sitarz3; @Sitarz2; @Sitarz1] and group field theory [@Oriti].

As a final issue related with $\kappa(\tau)$-deformation, we shall deal in this paper, is the possibility of extending the $\kappa$-deformations via twisting. Quantum deformations for Lorentz and Poincaré symmetries have been classified in terms of classical $r$-matrices [@Zakrz-Comm]. For example the original $\kappa$-deformation of Poincaré algebra corresponds to $r=M_{0i}\wedge P^i$. It is a particular case of more general family $r_\tau=\tau^\alpha M_{\alpha\mu}\wedge P^\mu$ found for any non-zero vector $\tau$ by Zakrzewski [@Zakrz-Comm]. It has been shown in the same paper that $r_\tau$ admits extensions $r_\tau+ \xi r^{\prime}$ with an additional parameter $\xi$, where $r^{\prime}$ corresponds to some specific triangular deformations. The passage from a classical $r$-matrix to the corresponding deformation is, in general, non trivial task even 