In the past two decades, deeply virtual Compton scattering of electrons has been successfully used to advance our knowledge of the partonic structure of the free proton and investigate correlations between the transverse position and the longitudinal momentum of quarks inside the nucleon. Meanwhile, the structure of bound nucleons in nuclei has been studied in inclusive deep-inelastic lepton scattering experiments off nuclear targets, showing a significant difference in longitudinal momentum distribution of quarks inside the bound nucleon, known as the EMC effect. In this work, we report the first beam spin asymmetry (BSA) measurement of exclusive deeply virtual Compton scattering (DVCS) off a proton bound in $^4$He. The data used here were accumulated using a $6$ GeV longitudinally polarized electron beam incident on a pressurized $^4$He gaseous target placed within the CLAS spectrometer in Hall-B at the Thomas Jefferson National Accelerator Facility. The azimuthal angle ($phi$) dependence of the BSA was studied in a wide range of virtual photon and scattered proton kinematics. The $Q^2$, $x_B$, and t dependencies of the BSA on the bound proton are compared with those on the free proton. In the whole kinematical region of our measurements, the BSA on the bound proton is smaller by 20% to 40%, indicating possible medium modification of its partonic structure.
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