Mixing helium and argon as the working gas for Atmospheric pressure plasma jets (APPJs) is expected to combine the advantages of both helium and argon plasma jets. This study used a two-dimensional axisymmetric fluid model to investigate the impact of downstream targets with different εr on the radial propagation range and distribution of reactive oxygen species (ROS) in He + Ar + O2 APPJ, with an argon volume fraction of 10%. The study finds that the radial propagation range of He + Ar + O2 APPJ on the target surface decreases with increasing relative permittivity of the downstream target. A smaller relative permittivity suppresses the axial propagation velocity of the ionization wave but increased the radial propagation range of reactive species on the target surface and their average density. A larger relative permittivity results in a faster axial propagation velocity of the ionization wave and increased the peak density of reactive species generated on the target surface, but shortens the radial propagation range of these species on the target surface.