I have read that Ice Follies naturalizes well in the south. It grows like gangbusters here. Bloom lasts well and gently fades to a pretty shade.
I had Carlton in zone 10 and it was excellent. Better lasting bloom than King Alfred. Multiplied nicely.

This Southern Living article suggests:

Surefire Daffodils for the South
These daffodils bloom dependably in most areas and increase with little care: ‘Avalon’, ‘Carlton’, ‘February Gold’, ‘Geranium’, ‘Hawera’, ‘Ice Follies’, ‘Jack Snipe’, ‘Jetfire’, ‘Minnow’, Narcissus odorus, ‘Quail’, ‘Saint Keverne’, ‘Salome’, ‘Tête-à-tête’, ‘Thalia’, and ‘Trevithian’.

Here is a link that might be useful: daffodil article

I have grown nearly all of the Southern Living recommendations here in central MS over the years. They are not all surefire.
Geranium is a good one, but it is late, and often the weather is hot by the time it blooms so the blooms don't last even a week. And the foliage is large and coarse. Takes forever to ripen.
Hawera is excellent here. It multiplies steadily. It blooms late too, but earlier than Geranium. Its flowers and foliage are small and delicate. Beautiful, but not showy at a distance.
Ice Follies is excellent. Of the large bloomed dafs I grow, it is definitely one of the best. It blooms early, so it lasts longer. The bloom color is a very pale yellow fading to white. Not the cheerful bright yellow of some, but still great.
Jack Snipe is very good. It's a smaller blooom, but reliable even under tough conditions. Not a fast multiplier where I have it, but it has to compete with tree roots. It's charming.
Jetfire has been a failure half a dozen times over the years. IF I get any blooms, they steadily decrease and die out over three or four years. Don't know why. Maybe it's my location. Maybe the bulbs were mis-named: not an unusual occurence.
Minnow is sweet. It's like Geranium in every way except the blooms are really tiny. Same pros and same cons as Geranium.
Saint Keverne is my favorite bright yellow, large flowering daffodil. It blooms in early mid season here, so the blooms last a good long time. It multiplies steadily. The blooms are exceptionally lovely too, in my opinion.
Tete a tete is so strong it can get to be a nuisance. It multiplies prodigiously and blooms early. The blooms are small but such a bright yellow that they show from a distance. It is a short plant. Excellent for edging. You can't beat it.
Thalia is my favorite white. Pure, clear white blooms. Reasonably small foliage. It persists, but its increase is slow. If you can put it in really good soil it will increase faster. It's only fault is its lateness in bloom. But if you want white flowers, you have to wait. They are all late.
Trevithian is another beautiful yellow bloomer. the blooms are mid sized and blooom mid season. They have lovely form and substance. It multiplies. It is very nearly as good as St. Keverne.
Carlton is very good. The flower form is not as pretty as others, but it does persist for years, and sometimes multiplies. Very large bloom. Very bright color.
My favorite is not in the list and that is Campernelle.This is a jonquil. I have found that any daffodil that is in the class of jonquilla is a very good bet for the Deep South. Campernelle is often my very first bloom of the season and because it is so early the blooms last sometimes a month. It makes clumps very fast and although the blooms are small, they come in such profusion and are such a bright yellow that they are very showy.
Avalanche or Seven Sisters gives the appearance of white, although it has yellow cups. It multiplies like mad, is early (it's technically a paperwhite) and long lasting. Its one fault is the coarseness of its foliage. Still, it is a dandy.
Gigantic Star has been something of a disappointment to me. At the very least it is not multiplying much. And it may be decreasing. Still, I have had it for more than five years, so I suppose I got my money's worth. The blooms are big for sure. Otherwise, there's nothing outstanding about it.
Honestly, if you can find someone who has a whole pasture or hedgerow of daffodils that have naturalized in your area. Beg some of those and take them home. They will be the VERY best ones you will likely find.

Over the years, I have come to look for earliness in new ones I buy. The flowers last longer and are the most cherished. By the time the late ones come, other things are blooming and the late ripening foliage is a nuisance.

Great information Donna. Thanks.

Thanks to both of you. I can confirm your responses by a talk I had with customer service at Brent and Becky's. I was looking for a good yellow that multiplies well and they recommended Carlton, St. Keverne and Gigantic Star.

I have planted Ice Follies and found it does well here in Central VA, being a very good perennializer even with our hot and often dry summers. I agree about the very pretty white daffodil called Thalia. It's a little slower, but it seems to do well enough even competing with a small tree.

Donnabaskets, your comment: "Tete a tete is so strong it can get to be a nuisance" is spot-on. It spreads so well that it's impinging on some areas near our front door that I want to fill in with the eye-catching "Ruby Giant" crocus.

CAN I PLANT DAFFODILS UNDER A SHRUB CALLED "WINTERBERRY"? It's not a densely foliaged shrub so sun will shine through the canopy of leaves. Is it a bad idea to ever plant them under shrubs due to competition? I always add a good bulb fertilizer to the planting area. I would like to do this next month so please reply back. Thanks much.

Thank you for the time you spent writing Donnabaskets. I'll keep it for a reference.

You certainly can. I tend to plant bulbs under and around virtually any shrub that loses its leaves, including roses. It is amazing how much better those areas look with green leaves and bright blooms. Then in the spring, the shrub's new foliage helps cover ratty looking bulb foliage that is ripening.