The observation of non-thermal radiation of SNRs are essential for elucidating the mechanism of particle acceleration. MAGIC and Fermi discovered very high energy (VHE) $\gamma$-ray radiation from the northern part of SNR G78.2+2.1 (MAGIC Collaboration.,2020).
This radiation is suggested to be originated from cosmic rays escaping from the SNR.
However, it is inconclusive since the electron energy distribution is not well estimated.
To solve this problem, we analyzed data from the X-ray astronomy satellite Suzaku to evaluate the contribution of the leptonic emission of the broadband spectrum of MAGIC J2019+408.
Our analysis revealed a hard X-ray component in the northern region of SNR G78.2+2.1 with a flux several times larger than the X-ray background radiation.
The emission extending outside the SNR was represented in the X-ray image in 2-5 keV, but is not associated with the SNR.
X-rays above 2 keV could be explained either by an absorbed thermal-emission model with a temperature of $1.6_{-0.2}^{+0.4}\,\rm{keV}$ and low-solar $\left(0.3\pm0.2\,Z_\odot\right)$ abundances or by an absorbed synchrotron $\left(\Gamma=3.7\pm0.5\right)$ radiation model with no statistically significant difference.
From SED analysis of radio to VHE $\gamma$-ray, X-ray and $\gamma$-ray spectra can be reproduced by the synchrotron model with the magnetic field strength of $50\,\rm{\mu G}$, but requires more-than one order-of-magnitude brighter radio flux than the observation result of the SNR shell.
Alternatively, a magnetic intensity of $4\,\rm{\mu G}$ will also satisfy radio and VHE $\gamma$-ray flux, but this magnetic strength was significantly lower than what we expected for the diffusive shock acceleration.
These results suggest that the observed X-rays have a different origin from non-thermal emission of MAGIC J2019+408, and some of the VHE $\gamma$-rays originated from escaped cosmic rays.