The case is called adessive and like in Irish, it's English meaning is "at". "Minulla on" = I have but also "pöydällä on" = there are __ at the house.

The suffix is "-lla" but thanks to Finnish being the bastard difficult language it is, it's sometimes "-llä" and the words of course change before you add the suffix (thus minä changes into minulla). I don't actually know why.

I'm so glad I never had to learn how to use all of these.