The process underlying differences in expression of a gene, according to which parent has transmitted, is called –
There are functional differences between paternal and maternal genes. So the expression of gene will be different depending on, whether it has transmitted by father or mother. This is called genomic imprinting
Anticipation

In genetics, anticipation is a phenomenon where by the symptoms of a genetic disorder become apparent at an earlier age as it is passed to next generation.
In most cases, an increased severity of symptoms is also noted.
Anticipation is seen in trinucleotide repeat disorders, e.g. Huntigton's disease, myotonic dystrophy, Fragile 'X' syndrome and Friedreich ataxia.

Mosaicism 

Mosaicism is the occurence of two or more different types of cell populations in the same individuals.
For example same individual have cells having 45X and 47, XXX, i.e. - 45 X / 47 XXX mosaic.

Nonpenetrance 

Some individuals inherit the mutant gene but are phenotypically normal. This is referred as nonpenetrance.
Anticipation
Masaicism
Non–penetrance
Genomic imprinting