This paper presents the extended results of measurements of $W^{\pm}W^{\pm}jj$ production and limits on anomalous quartic gauge couplings using 20.3 ${\rm fb}^{-1}$ of proton-proton collision data at $\sqrt{s}=8$ TeV recorded by the ATLAS detector at the Large Hadron Collider. Events with two leptons ($e$ or $\mu$) with the same electric charge and at least two jets are analyzed. Production cross-sections are determined in two fiducial regions, with different sensitivities to the electroweak and strong production mechanisms. An additional fiducial region, particularly sensitive to anomalous quartic gauge coupling parameters $\alpha_4$ and $\alpha_5$, is introduced, which allows more stringent limits on these parameters compared to the previous ATLAS measurement.