RAW: No metamagic can be applied to wish-duplicated spell effects except empowered (RAI disagrees)
Wish duplicates other spells, it doesn't cast them
Wish states that you can use it to:
...duplicate the effect of any other spell of 8th level or lower. You
don't need to meet the requirements of that spell, it simply takes
Note that it doesn't say anything about the fact that you are casting the spell. You aren't. You are casting wish and as the effect, getting the effects of another spell.
The rules for metamagic say:
You can only use one Metamagic option on a spell when you cast it, unless otherwise noted.
And every metamagic option except empowered spell begins with:
When you cast a spell...
Thus, you could apply metamagic to wish, but it would only apply to the duration and other characteristics of wish itself (since that is what you are casting), not the spell whose effects it is duplicating. At the exact time of casting wish only has the characteristics (range, duration, etc.) listed for wish and not the spell it is duplicating.
This effectively means that you can only apply Quickened Spell and Subtle Spell to wish, neither of which will affect the duplicated spell's effects. The only effect would be to be able to cast wish itself as a bonus action and without somatic or verbal components respectively.
Empowered Spell will work for any spell that wish duplicates that does damage
Empowered Spell says:
When you roll damage for a spell...
There are no other requirements than this, and this can clearly only be applied after the spell is cast and does not depend on having actually cast it. Thus, you can still empower any spell damage resulting from a wish-duplicated spell.
You can always wish for a metamagicked spell
Another option would be of course simply to wish for a spell with its metamagic effects. However, this would be outside the realm of duplicating a spell and into the custom wish territory. Thus it would come with the 33% chance of never being able to cast wish again.
RAI: Yes you can apply metamagic to wish-duplicated spells
Jeremy Crawford appears to differ on this interpretation in this Tweet:
Q: Can you Twin a spell duplicated with Wish? And if you do, how many sorcery points do you use.
A: Yes, and use the number of points appropriate for the level of the spell you are duplicating.
And again in the Sage Advice Compendium:
Can my sorcerer use Twinned Spell on a spell duplicated by the casting of a wish spell? And if so, how many sorcery points does it cost? Yes, you can. It costs the number of sorcery points appropriate for the level of the spell you’re duplicating.
It isn't really clear what logic JC uses to support this answer. It is possible he is implying that wish does actually result in the duplicated effects being cast, but that does not appear to follow the RAW. This might also have an impact on other effects that depend on the spell being "cast". But, if it makes more sense to you and your DM/table prefers, this ruling is there to be used.