In the unknown territory of transfermium nuclei, the relativistic mean-field (RMF) theory has been applied to probe decay modes which include $alpha$-decay, spontaneous fission (SF), and a less explored weak-decay. These decay modes are analyzed on equal footing for 101$leq$Z$leq$109 and as a consequence, the half-lives for weak-decay are indeed found comparable for several isotopes. Our prediction of decay modes and half-lives are found in excellent agreement with available experimental decay modes and half-lives along with the results of some other theories. Out of $alpha$, $beta^+$/EC, $beta^-$, and SF, the most probable decay mode is anticipated along with its half-life over a wide range of odd and even nuclei to frame a novel sight into terra incognita.
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