The correct noun form and what to say instead of “genuinity” is “genuineness”, which means “the quality of being honest or sincere.” Merriam-Webster states the noun form of “genuine” is “genuineness”, and there is no entry for “genuinity.”

The correct answer is “genuineness.” That’s the noun agreed to by dictionaries, and it’s the one most people use today. However, according to Googe N-Gram Viewer, “genuinity” is also in use today, but it is far less popular than “genuineness.” Things are a bit tricky, though.