The ricotta meant by the OP is an acid-coagulated cheese, like paneer. If I understand correctly, that's how "ricotta" is made in the States. In Europe, particularly in Italy, "ricotta" is a whey cheese made with the whey left over from rennet-coagulated cheese. The same kind of cheese is called urda in Romania and myzithra/ anthotyro in Greece.
I'm not sure you can really make mysost from the whey left over from acid-coagulated cheese. I used to make cheese by straining milk kefir. I made mysost/ brunost from the leftover whey a couple of times and it was intensely acidic. So much so that I used it as a thickener in soups, rather than eat it on my toast. If you want the silken, slightly tangy tofu butter style of mysost, then I don't think you can get it without whey from rennet cheese.