Forgot to add one more alternative that I found

Skyrocket Juniper

Pretty setting! I've had a Skypencil in my flower border for about 5 years and it hasn't grown very fast. Just my experience.
Are you looking for a slow, medium or fast growth rate?

I am ok with medium or fast. Just need a tree that is not affected in the winter as well as disease free

you are severely limiting yourself.. by what bigboxstore sells locally ... and that includes the 3 usual suspects you are listing ...

you can probably do so much better.. mail order ...

unfortunately.. this MI boy cant help you with selections for GA ...

call someplace like conifer kingdom

ken

Ok. I can mail odder as well.

A 3' max width and a 12' height limitation narrows down the choices substantially. And based on your list, I assume you want these to be evergreen as well.

The juniper will get taller and wider than your parameters plus the location looks bit to shady for junipers to be happy. In addition to the arborvitae and Sky Pencil (which I have never seen in a box store, btw) the following could work and if exceeding the intended height could certainly be pruned to stay within bounds:
Thuja occidentalis 'DeGroot's Spire' or 'Smaragd' (Emerald Green)
Ilex crenata 'Jersey Pinnacle'
Ilex vomitoria 'Will Fleming'
Euonymus japonicus 'Green Spire' (only gets to around 8' tall)
Cephalotaxus harringtonia 'Fastigiata'

I could suggest some yews (Taxus species) that could work but they grow SO slowly I'm not sure they are really what you are looking for. Same with boxwood.

And if you didn't mind a lot of pruning or shearing to keep size in check there are other broadleaf evergreen shrubs that could fit the bill.

Thank you for the suggestions

Yes, as gardengirl noted, there is a boxwood (at least one) which grows tall and narrow. I can't remember it's name, but I got one at a local nursery here in Georgia, so you should be able to find it, too. Incidentally, I also saw a Sky Pencil at the same nursery (Pike Nursery). I'm not a big fan of "traditional" boxwoods (in fact, they bore me to death), but this tall narrow one was quite nice, and I ended up with it instead of the Sky Pencil I had gone to buy.

There are several cultivars of columnar boxwoods available - 'Green Tower', 'Graham Blandy' and 'Dee Runk' are three that come to mind. But box tends to be rather slow growing......just saying :-)

The height requirement is more challenging than the width. It basically requires you to get a weeper or something like boxwood that can be sheered to size. If trained upright, I see no reason why Picea abies 'Pendula' wouldn't work in that space. Once it reached 10ft or so, you could allow it to weep back down to the ground away from the house, still keeping the narrow footprint for many years, until it eventually grew the 10ft back down...

If you get enough sun to make it worthwhile you could instead get Picea abies 'Gold Drift', but if not enough sun, it won't turn gold anyways, and just be an expensive Pendula.

@GG - They sell Skypencil Holly at Big box stores around here all the time. Must be a regional thing.

Sorry, I now think height is not that important. My worry is the width of the tree. I can plant a tree that can grow up to 20 feet or more. Thanks

All they sell at box stores around here are 'developer standards' or only the very most common plants. And things that are not the slightest bit winter hardy that they sell as perennials (shipped up from CA, I'm sure). I guess maybe there is too much competition from independent nurseries. It's pretty much just the non-gardeners here that plant shop at Home Depot or Lowes.

Ok... with the height limit removed here are a few to look at. I believe these are all ok in the south, but you would want to visit some arboretums to confirm:
Picea omorika 'Pendula Bruns'
Chamaecyparis nootkatensis ´Green Arrow´
Chamaecyparis lawsoniana 'Blue Surprise'
Chamaecyparis lawsoniana 'Barry's Silver'
Abies pinsapo 'Fastigiata'
Abies numidica 'Pendula'
Cephalotaxus harringtonia 'Fastigiata'
Thuja occidentalis 'Degroot's Spire'

I'm a little skeptical as to how well the 'Barry's Silver' would work. It's a dwarf selection that grows very slowly. The one in my old garden (here in the PNW where Lawsons do reasonably well) was only about 4' tall after about 6 years.

And do Lawson cypress do well in the heat and humidity of the South? If you go this route, make sure it is a grafted selection on Phytophthora resistant root stock.