What is exactly happening at the molecular level when two genes constitute incomplete dominance? Whether the protein formed from each of the genes constitute a new protein having a different function or anything happens at the RNA level of the two genes.
Molecular mechanisms of incomplete dominance (a.k.a. partial- or semi-dominance) vary. As an example, let's look at snapdragons and morning glories, two flowering plants that both exhibit incomplete dominance relative to flower pigmentation.
Snapdragons (Antirrhinum majus) have multiple alleles at the nivea locus. The wild-type nivea transcript (niv+) encodes a chalcone synthase involved in pigment biosynthesis, and a single copy of the niv+ allele is sufficient for wild-type pigmentation. However, niv+ is semi-dominant with the mutant niv-525 allele, leading to reduced pigmentation in the heterozygote. The original paper describing this effect offers some possible molecular explanations:
Transcription factor sequestration. The niv-525 allele could encode a defective enzyme. This allele also contains an inverted duplication of a transcription factor binding domain required for enzyme expression. The defective niv-525 allele therefore titrates away transcription factor from niv+, leading to less enzyme and therefore less pigment.
Transvection. There is some physical interaction at homologous positions on the chromosome, such that transcription of one or both alleles is interrupted. This could be realized as binding of the enhancer associated with the wild-type allele to the promoter of the defective allele. Figure 9 of this paper has a good explanatory graphic.
Anti-sense hybridization. The inverted duplication on the niv-525 allele contains a TATA box. Transcription initiated at this site would result in a transcript anti-sense to the wild-type mRNA. Hybridization of the sense and anti-sense RNAs creates dsRNA that is selectively degraded and/or inefficiently transported out of the nucleus, ultimately leading to less enzyme product.
Morning glories (Ipomoea purpurea) show similar genetics at the A locus, which also encodes a chalcone synthase. However, unlike the snapdragon niv+ allele, a single copy of the wild-type a allele is not sufficient to produce wild-type pigmentation. Therefore, incomplete dominance in morning glory results from a simple dosage-dependent mechanism, as described here.
Strictly speaking, incomplete dominance is an interaction between two alleles of the same gene not between two genes.
The most common cause of this is the dosage effect. For example, the product of CHS-D gene is an enzyme required for the synthesis of purple pigment anthocyanin in morning glory flowers. If a plant has two functional (A) alleles of this gene it produces enough pigment to have intensely purple flowers. The a allele has the loss-of-function mutation (isn't able to produce working enzyme) so homozygous a/a plants will lack purple pigment resulting in white flowers. But heterozygous A/a plants have half of the normal enzyme level and half of the pigment so the flowers are lighter purple (source). Genes like this are said to be haploinsufficient. In cases of full dominance, one functional copy of the gene is enough to produce a "normal" phenotype (the gene is haplosufficient) or the gene is upregulated to bring the concentration of functional products to the required level (source).
There are other mechanisms for incomplete dominance. For example, in snapdragon flowers, the allele niv-571 at nivea locus can inhibit the expression of "normal" Niv+ allele in heterozygous plants (source).
Dominance or Recessiveness is the characteristic of allele, not gene.
Particular gene contains data for producing specific protein. Protein produced from one allele can effect protein synthesis of other one. Protein formed from recessive allele can show dominance over the dominant allele, and this is known as Dominant negative.
The protein produced from one allele is faulty and prevents other allele's protein to work properly. Both the proteins interact with each other in particular cell.
Genetic trait for red hair is an example of dominant negative. Gene MC1R is responsible for red hair. Protein produced by this gene converts red pigment into brown. When this protein is faulty the red pigment is accumulated and hair appears red in colour. Usually red hair is recessive trait. Two faulty MC1R gene results in read hair characteristic. Both the proteins formed from MC1R gene need to bind so that red pigment converts into brown. But when functioning product binds with faulty one, the protein becomes defective. So this defective MC1R protein is responsible for showing dominance.