I live in zone 5b-6 Kansas and wonder if there was a Jasmine I could grow.
Have you looked into Winter Jasmine (Jasminum nudiflorum)?
I have no personal experience with this plant -- it would be cooked alive here in the desert -- but it sounds like it could work well in your zone.
Here is a link that might be useful: Winter Jasmine Planting Guide
Just dawned on me you're probably looking for something with fragrance.
This one doesn't have any; it blooms in winter and there are few (if any) insects to attract with scent. Sorry!
finchelover, you can grow jasmines in Zone 5-6 if you are willing to winter them inside. If you are looking for a jasmine hardy in the ground in 5-6, I don't believe there are any.
From what I have read Confederate Jasmine is not a true Jasmine but it has the same fragrance as a Jasamine and so far for 2 winters mine has come back. I purchased it at Home Depot 3 years ago. I grew it in a pot the first year and moved it to the garage the firt winter.
The next summer it started growing up the wall I planted it in the garden next to the house and it has come back. They say evergreen but it is not evergreen in my climate but it comes back and bloomed June -August.
I found the tag it says....
Confedertae Jasmine, Trachelospermum Jasminoides
HARDY TO 0 DEGREES MULCH 3"