The electron-capture decay followed by a prompt fission process was searched for in the hitherto unknown most neutron-deficient Md isotope with mass number 244. Alpha decay with α-particle energies of 8.73–8.86 MeV and with a half-life of 0.30+0.19−0.09  s was assigned to 244Md. No fission event with a similar half-life potentially originating from spontaneous fissioning of the short-lived electron-capture decay daughter 244Fm was observed, which results in an upper limit of 0.14 for the electron-capture branching of 244Md. Two groups of fission events with half-lives of 0.9+0.6−0.3  ms and 5+3−2  ms were observed. The 0.9+0.6−0.3  ms activity was assigned to originate from the decay of 245Md. The origin of eight fission events resulting in a half-life of 5+3−2  ms could not be unambiguously identified within the present data while the possible explanation has to invoke previously unseen physics cases.