What are genes that produce alternative expressions of a trait called

The answer should be allele(s).

Alleles are alternative forms of genes. For example in eye color, there is brown eye allele that produces brown eyes or blue eye alleles that produces blue eyes. 

However, note that there may be dominant or recessive alleles. Dominant alleles are always expressed, meanwhile, recessive allele is only expressed when there is no dominant allele existing. 

An example is let say brown eye allele is dominant and blue eye allele is recessive. The eye gene is controlled by 2 alleles. If I had one brown eye allele and 1 blue, my eyes will be brown, because brown eye allele is dominant.