In order to realize more sensitive eEDM measurement, it would be worthwhile to find some new laser-cooled molecules with larger internal effective electric field (E$_{eff}$), higher electric polarizability and longer lifetime of the eEDM measurement state. Here we explore the merits of mercuric monofluoride ($^{202}Hg^{19}F$, X$^ 2 {Sigma}_{1/2}$) for its potential of laser cooling and eEDM measurement. We theoretically investigated the electronic, rovibrational and hyperfine structures and verified the highly diagonal Franck-Condon factors (FCFs) of the main transitions by the Rydberg-Klein-Rees inversion (RKR) method and the Morse approximation. Hyperfine manifolds of the X$^ 2 {Sigma}_{1/2} ( u=0$) rotational states were examined with the effective Hamiltonian approach and a feasible sideband modulation scheme was proposed. In order to enhance optical cycling, the microwave remixing method was employed to address all the necessary levels. The Zeeman effect and the hyperfine structure magnetic g factors of the X$^ 2 {Sigma}_{1/2} ( u=0$,$mathit{ N } $=1) state were studied subsequently. Finally, its statistical sensitivities for the eEDM measurement were estimated respectively to be about $9times 10^{-31} ebullet cm $ (the laser cooled transverse beam experiment), $2times 10^{-31} ebullet cm$ (the fountain experiment) and $1times 10^{-32}$ ebullet cm (experiment with trapped cold molecules), indicating that $^{202}Hg^{19}F$ might be another promising eEDM candidate when compared with the most recent ThO result of $d_{ e } = (4.3 pm 3.1_{ stat } pm 2.6_{ syst })times 10^{-30} ebullet cm$ (Nature, 562, 355 (2018)). In addition, the possibility of direct Stark decelerating of the HgF radical was also discussed.
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