Thanks for writing. I'm sorry, but there's really not much you can do about the seedlings short of using a pre-emergence herbicide in your garden. The herbicide will stop many, but not all, from sprouting if you use it correctly.
Spreading a layer of mulch over your garden will also help suppress some of the seedlings from growing.
Look for a variety of these products at your local garden center.
---Justin, Senior Garden Editor, BHG.com