I think that may be chickweed.

It looks a lot like chickweed to me too, but it's very hard to tell. If it is, the OP should get it out before it goes to seed--and put it in the trash. Chickweed can flower and set seed after being pulled-and they are prolific seeders. Each plant, no matter how large it is, comes from one very thin stem.

Thank you both. it is not chickweed compare the pictures on internet.I don’t remember it flowers but definitely not white flower. I took more pictures today. hope they are more clear?

Compare to Lysimachia nummularia.

thank you gardengal48. I believe you nailed it. stores sale this as ground cover? welcome to my yard to dig :) seriously though, what is the best way to get rid of it? it’s stem rooted everywhere. thanks

It can be pretty rampant and I've only grown it in a container to cascade over the edge so never had to deal with ripping out from where it was not wanted.

It roots along the stems, so if happy can make a pretty dense clump that would be hard to remove by hand. But it should respond to pretty much any lawn broadleaved weed killer. Weed-B-Gon lists creeping jenny (the common name) as a target plant so you should be good to go with that.

Definitely Lysimachia nummularia. Unlike chickweed it’s perennial. Personally I would not try to fight it. It grows, as you say, in damp shade where grass would be a challenge. It’s evergreen, produces small yellow flowers and requires no care.

Does it grow faster than the grass or longr in the year or create any maintenance issues?

Back in 1960 it was an accomplishment to create a putting green in your new suburb house. Not now. Now the challenge is to create a low labor non monoculture lawn.

The area is between our swing set and the arborvitae. if leave it alone. it probably will take over the whole lawn. i did dig around to see how hard to get rid of them. not easy. May need to get the weed-b-gon.

I'm sure there are many ways to kill it, but unless you have something to replace it with, there's no point. Something just as bad will fill the void. If you would rather have a full lawn, you need to kill it, scrape off as much as you can once it's dead, exposing soil, and then put down shade lawn seed. Probably best to do this around labor day.