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If you are meaning to to ask if the Phoenix rooster breeds the large egg breeds, will it make there eggs smaller, then the answer is no, the size or breed of a rooster that fertilizes an egg will not affect the size of the egg that is laid, the egg will be the same size as it normally would be from that particular hen, even if it wasnt fertile.
But if you are talking about the female offspring from that Phoenix rooster on the large breed hens, then yes their eggs should be more of a medium size.