Hi Dr. Andross - Thanks for your question.  I too have this problem weed that keeps popping up where I don't want it.

This weed is called Creeping Woodsorrel.  It has two variations - Oxalis corniculata has greenish leaves and Oxalis corniculata var. atropurpurea has purplish leaves with yellow flowers.

 It definitely looks like a traditional clover and is, as you well know, very persistent!

Here is some information on this weed with some options to try to control it - https://ipm.ucanr.edu/PMG/PESTNOTES/pn7444.html. Check out the Management - Landscape Plantings - Creeping Woodsorrel section for control suggestions.

Good morning Norm - Diligent weeding is the way to handle the existing weeds in and around the jasmine as any broadleaf herbicide will damage or kill the jasmine too.

Here is some information from the Pacific Northwest Weed Management Handbook about weed control in home landscapes - https://pnwhandbooks.org/weed/horticultural/home-garden-landscape-management/management-tactics.    Take a look at Chemical Control Strategies #1 Preemergent herbicides applied selectively to soil.   Take note of the section on using corn gluten meal.  I have used it in flower containers on my deck and it has helped to prevent weed seeds from growing.  You do need to reapply at times after rain for example.   It is a non-chemical method to try.    
If you do try out one of the preemergent herbicides listed in the PNW handbook, please read and follow all label instructions.  Make sure it is listed as safe for your existing plants.   If the label  doesn't list your plant specifically, it strongly recommends testing it out on a small sample area to check for toxicity.

Best of luck with your weed battle.  Regards,  Bill