A study of the associated production of a (Z) boson and a charm quark jet ( (Z+c) ), and a comparison to production with a (b) quark jet ( (Z+b) ), in (pp) collisions at a centre-of-mass energy of 8 (\phantom{\rule{0.166667em}{0ex}}\text{TeV}) are presented. The analysis uses a data sample corresponding to an integrated luminosity of 19.7 (\phantom{\rule{0.166667em}{0ex}}{\text{fb}}^{-1}), collected with the CMS detector at the CERN LHC. The (Z) boson candidates are identified through their decays into pairs of electrons or muons. Jets originating from heavy flavour quarks are identified using semileptonic decays of (c) or (b) flavoured hadrons and hadronic decays of charm hadrons. The measurements are performed in the kinematic region with two leptons with ({p}{T}^{\ell }>20\phantom{\rule{0.166667em}{0ex}}\text{GeV}), (|{\eta }^{\ell }|<2.1), (71<{m}{\ell \ell }<111\phantom{\rule{0.166667em}{0ex}}\text{GeV}), and heavy flavour jets with ({p}_{T}^{\text{jet}}>25\phantom{\rule{0.166667em}{0ex}}\text{GeV}) and (|{\eta }^{\text{jet}}|<2.5). The (Z+c) production cross section is measured to be (\sigma \left(pp\to Z+c+X\right)B\left(Z\to {\ell }^{+}{\ell }^{-}\right)=8.8±0.5\phantom{\rule{0.166667em}{0ex}}\text{(stat)}±0.6\phantom{\rule{0.166667em}{0ex}}\text{(syst)}\phantom{\rule{0.166667em}{0ex}}\text{pb}). The ratio of the (Z+c) and (Z+b) production cross sections is measured to be (\sigma \left(pp\to Z+c+X\right)/\sigma \left(pp\to Z+b+X\right)=2.0±0.2\phantom{\rule{0.166667em}{0ex}}\text{(stat)}±0.2\phantom{\rule{0.166667em}{0ex}}\text{(syst)}). The (Z+c) production cross section and the cross section ratio are also measured as a function of the transverse momentum of the (Z) boson and of the heavy flavour jet. The measurements are compared with theoretical predictions.