We assume a simple power-law model, $$\frac{dN}{dE}=F_0 (\frac{E}{E_{\text{dec}}})^{-\Gamma},$$ where $E_{\text{dec}}$ and $F_0$ are the decorrelation energy and differential flux at $E_{\text{dec}}$, and $\Gamma$ is the spectral photon index. The spectral parameters are obtained via forward-folding using Poissonian maximum likelihood procedure described by @2017MNRAS.472.2956A. In order to calculate the intrinsic spectral parameters, the same estimation procedure is used by assuming $z=0.35$ (see Sect. \[sec3-5\]) and Extragalactic Background Light (EBL) absorption model described by @2011MNRAS.410.2556D. The spectral parameters are summarized in Table \[tab\_tev\_spec\] for the flare night and the average spectrum. The fitted model statistics are calculated in the energy range of 65–370GeV and 65–250GeV for average and flare night spectra, where MAGIC detected the source.

High-energy gamma rays {#sec3-2}
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We have found that there is no significant HE gamma-ray spectral and flux variability on a daily basis during the investigated period (MJD 57220–57240). These results are shown in Figure \[fig\_lc\] (Panels b and c). The HE gamma-ray constant fit flux is $F_{(0.1-300\,\text{GeV})} = (1.4 \pm 0.4) \times 10^{-7}$phcm$^{-2}$s$^{-1}$, which is $\sim\,2$ times higher than the average flux reported in the 3FGL catalogue [@2015ApJS..218...23A] for this source.

To model the HE gamma-ray spectrum of S2 0109+22, a power-law function which uses 