is a peculiar TeV complex with a morphology changing from a diffuse source ( at $ 2$ TeV to a point-like one ( at $ 10$ TeV energies. The morphology and spectral properties of could be understood in terms of (diffusive) hadronic or leptonic models in which the observed TeV emission arises correpondingly from proton-proton or IC-radiation of relativistic particles present in the region. In this work, we perform searches of the X-ray counterpart of the source originating from the synchrotron emission of the primary or secondary relativistic electrons produced within leptonic or hadronic models. Such an emission can be extended and remain beyond the detection capabilities of narrow field-of-view instruments such as We utilised the publicly available first-6-months eROSITA dataset (DR1) fully covering the selected analysis region of $>5^ around We discuss biases connected to variable plasma temperature or neutral hydrogen column density in the region and present results based on the background modelling approach. The performed analysis does not allow us to detect the extended X-ray counterpart of of $0.07^ sizes. The derived upper limits are significantly higher than the expected hadronic model flux of the X-ray counterpart. For the leptonic model, the derived limits indicate the magnetic field in the region $B We argue that further advances in the diffuse X-ray counterpart searches could be achieved with either next-generation missions or Msec-long observational campaigns using currently operating instruments.
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