Hi there Linguisa530,
For a lot of beekeepers mice are only a concern as temperatures begin to drop and bees become less active. Mice can then slip into hives more or less undetected. The location of your hive may also be making it more of a desirable space for mice to nest.
In your top bar hive I would recommend utilizing just as much space as the bees need by flanking their active hive space with divider boards on either side of their hive space. To prevent mice from getting into the opposite side of the hive I would make sure all unused top bars are in placed along the top of that cavity to prevent mice from gaining access. When all the top bars are in place you may still have a small gap between your last top bar and the trapezoidal end piece of your top bar hive (the gap is to allow your for the wider honey combs that bees make during honey ripening). I would recommend covering this gap with hard ware cloth or a cut piece of wood. That should prevent the mice from gaining access to that side of the hive. Make sure both of you entrances are also closed if they are both on the non-active hive side.
To address the problem of the mice nesting above the top bars you will need to block there access to the hive around the roof. The roof telescopes over the edge of the actual hive body in a top bar hive. This is to allow air flow, and prevent rain water from seeping into the hive space, however the space is large enough for a crafty mouse to squeeze underneath into the roof on top of the top bars.
I would recommend attaching a piece of hardware cloth (cut into a strip) to your roof edge on both the entrance board, and window board sides of your hive. This will still allow for air flow into the hive but prevent the mice from gaining access to that cavity. You could also potentially block the space with something like polystyrene cut to fit and then wedged into that space. You would just need to make sure that space is not collecting too much heat, or find some way to adding venting channels. You can find hardware cloth or insulation foam boards at any larger hardware store. Number 4 hardware cloth will block mice, numbers 7 and 8 will block bees from passing as well if you are interested in making the space impassable to bees.
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