I've got a vegetable garden in my back yard. Back in the fall I planted some (I think) serrano seeds that I took out of a store-bought pepper. Nothing came up, so I overseeded with beets. Fast forward to a month ago, and what looked like a pepper plant popped up. Then another came up in roughly the same row a few feet away. The plant looks to me like a pepper, but the flowers and fruits don't seem quite right. I've been told that peppers will cross-pollinate with other types of peppers, which could lead to odd-looking hybrids.
The plants are multi-stemmed, upright, and bushy. They're currently about 2' tall. Most of the leaves look like regular pepper leaves, but there are also some leaves that have serrated edges. The flowers are about 1/4" in diameter, white petals, yellow centers, held downward, and are in clusters of 3-5 on short stalks that come out from the stem. The fruits, at this point, are very small and round. They don't seem to be growing much, even though they've been on the plant for probably 2 weeks.
If you need different photos or have questions that will help answer my question, please ask! I just hope I haven't been coddling weeds.
P.S. There's a third plant that's really just single-stemmed, although it's started to branch now. Its leaves are mostly serrated, compared to the other two plants who's leaves are mostly non-serrated.