The new tissue resulting from fertilization is genetically different from that which comes from the mother plant. This means that, for different genetic structures resulting from different fertilization combinations, the embryo tissue will produce different compounds.
Key compounds are hormones, which will move from the embryo to the other tissues of the fruit, and even to tissues out of the fruit itself. Different levels of auxins will result in different growth rates in the ovule wall, for example, which develops in some plant species into fruit flesh. Other hormones will also affect the growth rate in addition to the differentiation of these tissues.
Yes, the quality of fruit is influenced by pollen parents.
Horticulturally, Yes, The concept of metaxenia may applicable here to change the qualitative aspect.
Physiologically, Yes, the ability to produce auxin during fertilization. The pollen pistil interaction affects the fertilization as well and so on the quality of fruit.
Yes Sir, the quality of fruits is surely influenced by pollen parents as the source of pollen directly affects the growth of ovary tissues by inducing hormone production which exerts specific effects on the fruit quality and growth. Cross-pollination may cause more strong embryos in comparison to self-pollination due to genetic depression.
And metaxenia occures at self pollinated plants too (if there is a pollinator). The bigger the genetic distance between the two parents, the bigger the difference.