There are some good remarks on this point by Routh (who is quoted in 'Supernatural Religion' _apparently_ as adverse to the genuineness of the fragments).
He says: 'There seems to me to be nothing in these extracts to compel us to deny the authorship of Apollinaris.

Nor must we refuse credit to the author of the Preface [to the Paschal Chronicle] any more than to other writers of the same times on whose testimony many books of the ancients have been received, although not mentioned by Eusebius or any other of his contemporaries; especially as Eusebius declares below that it was only some select books that had come to his hands out of many that Apollinaris had written' [Endnote 247:2].

It is objected (2) that Apollinaris is not likely to have spoken of a controversy in which the whole Asiatic Church was engaged as the opinion of a 'few ignorant wranglers' A fair objection, if he was really speaking of such a controversy.
But the great issue between the Churches of Asia and that of Rome was whether the Paschal festival should be kept, according to the Jewish custom, always on the fourteenth day of the month Nisan, or whether it should be kept on the Friday after the Paschal full moon, on whatever day of the month it might fall.

The fragment appears rather to allude to some local dispute as to the day on which the Lord suffered.

To go thoroughly into this question would involve us in all the mazes of the so-called Paschal controversy, and in the end a precise and certain conclusion would probably be impossible.
So far as I am aware, all the writers who have entered into the discussion start with assuming the genuineness of the Apollinarian fragment.
There remains however the fact that it rests only upon the attestation of a writer of the seventh century, who may possibly be wrong, but, if so, has been led into his error not wilfully but by accident.
No reason can be alleged for the forging or purposely false ascription of a fragment like this, and it bears the stamp of good faith in that it asks indulgence for opponents instead of censure.