What is this (seed/berry)-like object and where is it coming from?
Barring further details or photos, your fruits remind me of the drupe  from a hackberry (Celtis spp.)  tree. 



Hackberry drupes are relatively small, often being only about 6-10mm in diameter. 

Examples:
1, 
2. 

Do you have any warty looking trees nearby? 
(like this). 

Do you ever see the fruits in a different color? (purple, black, red, orange)?