I planted 12 pieces of potatoes ~2-3 weeks back and see few sprouts but don't know if they are weeds or actually the potato plants. The plants look like this:
Sorry, neither is a potato plant.
A potato sprout is medium to dark green (sometimes with reddish undertones just when breaking through), looks like a little whirl of wrinkly, thick leaves, then unfolds to the typical compound leaf.
The first plant in your post is probably a wood sorrel or oxalis, the second a clover. Without flowers and more details a precise id is near impossible, but I can at least tell you that these are not your potatos.
Many gardeners would pull them up as weeds immediately, you can enjoy the flowers first, then pull before they go to seed - or use your own judgement.