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Recently there is a resurrection in the study of heavy quark bound states ina hot and baryonless matter with an ambient magnetic field but the matterproduced at heavy-ion collider experiments is not perfectly baryonless, so wewish to explore the effect of small baryon asymmetry on the properties of heavyquarkonia immersed in a strongly magnetized hot quark matter. Therefore, wehave first revisited the structure of gluon self-energy tensor in the aboveenvironment to compute the resummed propagator for gluons. This resummedpropagator embodies the properties of medium, which gets translated into the(complex) potential between $Q$ and $\bar Q$ placed in the medium. We observethat the baryon asymmetry makes the real-part of potential slightly moreattractive and weakens the imaginary-part. This opposing effects thus lead tothe enhancement of binding energies and the reduction of thermal widths of $Q\bar Q$ ground states, respectively. Finally, the properties of quarkonia thusdeciphered facilitates to compute the dissociation points of $J/\psi$ and$\Upsilon$, which are found to have slightly larger values in the presence ofbaryon asymmetry. For example, $J/\psi$ is dissociated at $1.64~T_c$,$1.69~T_c$, and $1.75~T_c$, whereas $\Upsilon$ is dissociated at $1.95~T_c$,$1.97~T_c$ and $2.00 ~T_c$, for  $\mu=0, 60$ and $ 100 $ MeV, respectively. This observation prevents earlydissociation of quarkonia in the matter produced at ultrarelativistic heavy ioncollisions with a small net baryon number, compared to the ideal baryonlessmatter.

Heavy quarkonia in a baryon asymmetric strongly magnetized hot quark matter