Are you looking for clematis species that will bloom during different times of the year so that you have year long flowers? Or are you just looking for an evergreen clematis? Clematis armandii is a hardy evergreen, but it blooms from march through april and a little in the summer in most areas, though I have heard of some people who's bloom late winter. Clematis cirrhosa willl bloom in late fall and into winter some, and there are many varieties that you an choose from to bloom between early spring and late summer. I'm not sure about late winter though, and a lot depends on where you live.
Well Clematis cirrhosa should bloom late fall to early/mid winter. There are may varieties that will bloom in spring, summer, and fall. And depending on the zone you are in, there may be a variety or two that will bloom in late winter.
I get your hardiness zone as 8, so it might be possible to have a clematis bloom every month, especially if you have a greenhouse or conservatory.
This UK site has hundreds of Clematis listed with the bloom times for the UK. Not sure if you can search by month of bloom, but it's worth a try.
https://www.clematis.hull.ac.uk/