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_{-0.09}^{+0.19} s was assigned to ^{244}Md. No fission event with a similar half-life potentially originating from spontaneous fissioning of the short-lived electron-capture decay daughter ^{244}Fm was observed, which results in an upper limit of 0.14 for the electron-capture branching of ^{244}Md. Two groups of fission events with half-lives of 0.9_{-0.3}^{+0.6} ms and 5_{-2}^{+3} ms were observed. The 0.9_{-0.3}^{+0.6} ms activity was assigned to originate from the decay of ^{245}Md. The origin of eight fission events resulting in a half-life of 5_{-2}^{+3} ms could not be unambiguously identified within the present data while the possible explanation has to invoke previously unseen physics cases.