The conversion between photons and axionlike particles (ALPs) in the Milky Way magnetic field could result in the detectable oscillation phenomena in $gamma$-ray spectra of Galactic sources. In this work, the GeV (Fermi-LAT) and TeV (MAGIC/VERITAS/H.E.S.S.) data of three bright supernova remnants (SNRs, ie. IC443, W51C and W49B) have been adopted together to search such the oscillation effect. Different from our previous analysis of the sole Fermi-LAT data of IC443, we do not find any reliable signal for the photon-ALP oscillation in the joint broadband spectrum of each SNR. The reason for the inconsistence is that in this work we use the latest revision (P8R3) of Fermi-LAT data, updated diffuse emission templates and the new version of the source catalog (4FGL), which lead to some modification of the GeV spectrum of IC443. Then we set constraints on ALP parameters based on the combined analysis of all the three sources. Though these constraints are somewhat weaker than limits from the CAST experiment and globular clusters, they are supportive of and complementary to these other results.
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