The triple test cross analysis was used to study different components of genetic variation by using 75 triple test cross families and their parents, F1 and F2 in one cotton cross (Giza 95 x Australy) for yield, its components and fiber quality traits. The 75 TTC families (25L1, 25L2 and 25L3) were sown at Sakha Experimental Station; Agriculture Research Center, Kafr El-Sheikh government; Egypt. Mean squares between L1, L2 and L3 were highly significant for all traits studied, while between L1 and L2 Families found to be significant for boll weight, lint percentage, lint index, fiber length and micronaire reading. Overall epistatic gene effects were highly significant differences for all traits studied except for fiber length and fiber strength. The (i) fixable type (additive × additive) was the most important epistatic effect than j and 1 non-fixable type for all traits. Both additive and dominance components were highly significant for all the traits studied. The degree of dominance was less than unity and confirmed the presence of partial dominance for all traits studied except for lint yield/plant; lint index and seed index were over-dominance. The Additive gene action played an important role in controlling inheritance for all traits studied than dominance one except for lint yield/plant; lint index and seed index. Direction of dominance (r) was non-significant for most traits indicating absence of dominance directional. Due to influence of (i) type of epistatic effects for the majority of the studied traits selection in early generations may be recommended. Genotypic correlation was positive and significant between yield traits and its components. This could help cotton breeder to use indirect selection to increase yield traits. All the studied traits showed higher proportion of recombinants inbreds falling outside parental range nearly 40%. So, these higher values of prediction revealed that it would be feasible to predict as early as possible for transgressive segregation which can surpass parental range for most studied traits.