I think what you have is some type of citrus tree maybe lime, not a jasmine plant. Citrus trees do have jasmine-like smelling white blooms, then later the fruits appear. I have a calamondin tree which bears smaller green fruits, and the tree smells so good when in bloom.
On the other hand, your plant seems to be vining, so it maybe a jasmine, have read this article and it talks about their jasmine that had fruits and in the article it was called Stephanotis floribunda.
http://www.evilmadscientist.co...
