I'm currently up to all of this researching in the genetics of pets I wanna keep. There, in one of my dragonesses (=female dragon) I noticed that she's got the recessive gene "Color: Red" and behind that is a little yellow star. I think this can occur on every gene so I'm asking:

What is the meaning behind this little star?

The star means she has a deviant color. Most Red dragons are simply red, but yours is copper and green because of a rare mutation that may occur when a pet is born with two of the same color or pattern genes, causing them to look differently. (You can check out all possible deviant appearances by going to the Skin Library.)

The star next to the color gene indicates that the color gene is deviant, rather than the pattern gene. Also, children cannot inherit this star, it only occurs randomly when the conditions are met.