Quebec Militia War of 1812 Cross belt plate

I was wondering if anyone was able to give me a bit of information in regards to this cross belt plate. It is War of 1812 era from the Quebec Militia. Does anyone know if this was worn by all the militias in the Quebec City area or just a single unit named Quebec Militia. The 1775 battle honour, from what I have read, was bestowed on this unit in 1808. Is there any reference for this unit? Any information would be appreciated.

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