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Can anyone help me identifying the bottom bracket? It had a cottered crank arm but only on one side, the other side has nothing.
I have no idea how to remove the spindle. I already tried hammering it out but it doesn't really move. I found nothing on the internet so far featuring this bottom bracket.
The part with the red arrow needs to be turned - as Daniel R Hicks has said
righty-loosy instead of righty-tighty
Your bottom bracket appears to be a variation on the Thompson bottom bracket.
The Thompson bottom bracket uses adjustable spindle cones and cups pressed into the bottom bracket shell like the Ashtabula bottom bracket. Unlike the Ashtabula crank, the non-drive side crank is removable, allowing for a smaller bottom bracket shell. Frames with either Italian or English bottom bracket shell diameters (independent of threading) may be fitted with Thompson bottom brackets.
Wikipedia
Here's a picture to give you some idea of what it looks like apart.
Here is a video of working on something similar.
