US (land of the free)
I have found what to me are serious contradictions. Two books that I am sure you have:
"Conversations with Yogananda" pg.110
"Autobiography of a Yogi" pg. 290 and pg.345
These three references taken together show a serious contradiction in my opinion.
If Yogananda claimed to be an avatar, he says in his autobiography that an avatar casts no shadow. But, on pg. 345 of the same book there is a picture of him clearly casting a shadow on the ground.
Dear Friend, your question is far less serious than perhaps you may feel. Slightly humorous even, as I can imagine a twinkle in Yogananda’s eye upon being "challenged".
As his own writing suggests the Upanishads contains minute classifications and the characteristics of the avatar are described by him as symbolic. These traits are not unlike so many others in spiritual traditions, e.g., being born of a virgin, or conceived without sin (immaculate conception).
This is not to deny that such beings do not, perchance, or at times, manifest such divine characteristics but to use Yogananda’s own words an avatar is not subject to the universal economy but this also means is not compelled to manifest the divine one either.
By contrast to an avatar such as Babaji, whose manifestation of "miraculous" powers comes part and parcel with his role, Yogananda’s role was to walk among men, to go to the skeptical West. Were he to have manifested such powers he would of course have been quite a sensation in the West but that is not usually God’s way of drawing souls to Him. Babaji, after all, has drawn a cloak of secrecy about him and is not accessible to the public.
So fret not, friend, that Paramhansa Yogananda did not actively demonstrate such traits. Look to his grace for signs of his spiritual power. These are found only in the heart open to his love.