The quark susceptibility $chi_q$ at zero and finite quark chemical potential provides a critical benchmark to determine the quark-gluon-plasma (QGP) degrees of freedom in relation to the results from lattice QCD (lQCD) in addition to the equation of state and transport coefficients. Here we extend the familiar dynamical-quasiparticle model (DQPM) to partonic propagators that explicitly depend on the three-momentum with respect to the partonic medium at rest in order to match perturbative QCD (pQCD) at high momenta. Within the extended dynamical-quasi-particle model (DQPM$^*$) we reproduce simultaneously the lQCD results for the quark number density and susceptibility and the QGP pressure at zero and finite (but small) chemical potential $mu_q$. The shear viscosity $eta$ and the electric conductivity $sigma_e$ from the extended quasiparticle model (DQPM$^*$) also turn out in close agreement with lattice results for $mu_q$ =0. The DQPM$^*$, furthermore, allows to evaluate the momentum $p$, temperature $T$ and chemical potential $mu_q$ dependencies of the partonic degrees of freedom also for larger $mu_q$ which are mandatory for transport studies of heavy-ion collisions in the regime 5 GeV $< sqrt{s_{NN}} <$ 10 GeV.
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