Compare to Houttuynia cordata. Goes nuts in moist, full sun areas, but grows in part shade as well.
hortster

I have this growing everywhere. It is very hard to get rid of.

What kind of flower does this get. It looks more like Nightshade or wild Morning Glory to me.
Both have extensive root systems that need to be pulled out.

Since you don't want it, shovel up the roots to get rid of whatever it is. If there are orange/purple potatoes, it's sweet potato. I doubt that's what it is since they are still dormant here. If it's Houttuynia, you can't garden that spot until you get rid of this. Little pieces of root not found/removed can keep growing new plants. Smothering might work for you. Can you add a pic of the whole area?