Space requirement to sponsor mother on Schengen visa to Germany

The answer is that you need an amount of space that is appropriate to put your mother up for 3 months. That isn't going to be a fixed amount, but you need to show an amount that would be considered normal.

For example if you have an unoccupied guest bedroom that your mother could sleep in, a kitchen big enough to prepare meals for everyone in the house plus her, and space for a table where you can eat together, that's almost certainly going to be fine. If you are living in one room, where there is no space for a second bed, and no kitchen, that's almost certainly not going to be OK.

If your space available is towards the bottom end of that, and especially if you don't have a bedroom where your mother can sleep, you are going to have to explain how the living arrangements will work.

You are also going to need to show that your living arrangements allow for your mother to stay. For example, if you are renting an apartment showing that your landlord is OK with your mother staying with you for 3 months.