A picture or drawing may help some. Depending on where you live, you may be able to find a structural engineer that could give you an opinion. It wouldn't be all that expensive unless you wanted drawings, certifications, etc. I did this when I discovered a problem when remodeling, and it only cost me about $100. He came over, looked things over, took some measurements, and went home. Called later after he'd made some calculations, and told me what I could do. As I said, though, if you need drawings, and certified, stamped, approved plans, it would boost the cost considerably. A wall sitting on a joist, rather than crossing them, is probably not a load-bearing wall. That doesn't mean you can just arbitrarily cut things...you'd first want to support the joists, then cut, then reinforce. Whether that would require simiply sistering things, or a header, or what, is hard to tell without more details. If that mod ever needed to be inspected, there are some fairly strict rules about the pitch and run of a set of stairs.