No, in that sentence you can't use "wish" instead of "hope". A wish for the future is expressed with the verb "hope". Yes, you can use "ever" in the way you used it.
We would say "I hope you never reject me again" or "I hope you won't ever reject me again".
I’m aiming to put this in a card as my wishes for the new year and send it to that person who rejected me once in the past.
So now I’m not sure which sentence to select.?