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We study the motion of uncharged particles and photons in the background of amagnetically charged Euler-Heisenberg (EH) black hole (BH) with scalar hair.The spacetime can be asymptotically (A)dS or flat. After investigating particlemotions around the BH and the behavior of the effective potential of theparticle radial motion, we determine the contribution of the BH parameters tothe geodesics. Photons follow null geodesics of an effective geometry inducedby the corrections of the EH non-linear electrodynamics. Thus, afterdetermining the effective geometry, we calculate the shadow of the BH. Uponcomparing the theoretically calculated BH shadow with the images of the shadowsof M87* and Sgr A* obtained by the Event Horizon Telescope collaboration, weimpose constraints on the BH parameters, namely the scalar hair ($\nu$), themagnetic charge ($Q_{m}$) and the EH parameter ($\alpha$).

Motion of particles around a magnetically charged Euler-Heisenberg black hole with scalar hair and the Event Horizon Telescope