Hello!

What you have is Creeping Charlie.  I have it and it is very hard to control but possible.  The first step is to get rid of the plant's favored environment.

Creeping Charlie thrives in moist, shady spots such as under trees and shrubs. If you can alter these conditions, it will be easier to discourage this weed. If possible, improve soil drainage or water less frequently, or prune trees up so the area receives more light.

Here is a site that will give you complete control steps including herbicides you can use,
https://extension.illinois.edu/lawns/managing-creeping-charlie-lawns

Do note that it will take a few years of repeated effort to control the weed and it is likely it will persist is some parts of your yard.

Please let us know if you have any other questions.  Good luck and thank you for contacting us!

Thank you very much for the reply.  Too bad it's so hard to control but I'll make an attempt!