It's mold. Identifying exactly what kind is a job for a biologist specializing in molds; it's not trivial to do.
There are soil fungicides... your local garden center probably has them. Also, it's a good bet you're overwatering; most molds like very damp conditions. If you can set the pot outside in the sun for a bit, that will probably help considerably even without the fungicide.
Don't store potting soil in an airtight container because potting soil is moist. The potting soil will grow mold if you do this. Just keep it in the bag you bought it in and tie the top shut.
A good potting mixture for plants include three parts of leaf mold soil and one part sand to maintain porosity.
The seeds from a pepper without mold will be better for use in recipes. Seeds used for planting should also be mold-free, ensuring a healthy plant.
It is best to use sterile soil in pots so that the seeds to not die from bacteria or mold. Once the seedling is established, it can be hardened off by exposing the plant to more light and perhaps cooler temperatures. Then it can go into garden soil that has bacteria and organic material.
Throw it away!
Mold is and always has been an element of our outside and inside environment. We breathe mold spores (sort of like the seeds of mold) in the outdoors air every day. And because outdoor and indoor airs are related, we will be breathing some of the same spores indoors. The mere existence of airborne mold spores in a residence or business is not necessarily a predicament. Some people, including the very young, adults with compromised immune systems, and people with mold allergies may be more susceptible to mold growth and may experience health problems as a result.
the water and the seeds
Put the seeds in a paper envelope. If you put them in a sealed container, use something to prevent mold.
Mold requires moisture, food and air. Since many building materials that a makes up a house is organic matter that is food for mold, the easiest way to minimize mold growth is to minimize moisture indoors.
Molds produce tiny spores to reproduce. Mold spores waft through the indoor and outdoor air continually. When mold spores land on a damp spot indoors, they may begin growing and digesting whatever they are growing on in order to survive. There are molds that can grow on wood, paper, carpet, and foods. When excessive moisture or water accumulates indoors, mold growth will often occur, particularly if the moisture problem remains undiscovered or un-addressed. There is no practical way to eliminate all mold and mold spores in the indoor environment; the way to control indoor mold growth is to control moisture.
To keep soil from compacting, do not walk on it. Lay it down, and leave it. Do not step on it, or pat it down. This will cause it to compact, and mold together.
Topsoil can be turned into a nutrient-rich potting soil by baking it in the oven. Baking topsoil kills harmful bacteria and mold spores. Spread a layer of topsoil onto a baking sheet and bake at 180 degrees for around 10 minutes.