Wish 's Immunity trumps Anti Magic Field 's suppression
There's no paradox. Wish has to be affected by Anti Magic Field to be suppressed. That suppression can't happen because the Wish is immune, so the Wish functions as normal.
Let's consider a fabricated analogy:
You're wearing the Armor of Protection From Sundering. It keeps you safe from giant hammers and stuff, and also grants you and your equipment immunity against effects that would specifically destroy them.
Your opponent is wielding the Axe of Sundering. It destroys the armor of anyone it hits. He hits you.
What happens is that your armor doesn't break. If the armor was already broken, then the axe could affect it, true, but as long as the armor isn't already rendered ineffective the axe can't do anything. Your armor is immune to the effects of the axe, but nothing makes the axe immune to the effects of your armor. The same thing is true in your question proper: Wish is immune to the effects of Anti Magic Field, but Anti Magic Field is not immune to the effects of Wish.
N.B. This answer assumes that the immunity to antimagic field you postulate in your question is relevant, viz. that the immunity will in fact protect the Wish spell. This may not be the case! It is reasonable for a GM to rule, as you seem inclined to, that a character who is by nature 'immune to Anti Magic Field' who wields, for example, a +2 flaming longsword would be able to employ the sword's magic powers within such a field. It would also be reasonable to rule, however, that it is the sword and not the character who must be immune for the sword to function. In the latter case you will have some difficulty making Wish's immunity relevant, although it may still be possible to do so. In any case, as long as the immunity is relevant, this answer stands, and the best way to discern if it's relevant or not is going to be to ask your GM.