clive,
Wax myrtle.
But the first year, you must mulch and water them.
Anything you plant won't grow in good without a decent amount of care the first couple of years.
They grow fast, when they are established, they don't really need alot of water, and if you want to trim them, they can take a beating and grow back more beautiful.
They are a native.
Look up online, you can find them anywhere.

Oleander is poisonous and I guess it is not recommended in residential areas

I wonder if Chinese Photinia (Photinia serrulata, P. serratifolia) might work. Hard to find sometimes. But I don't think deer like it. Then again, it depends how hungry they are.

Another choice is Ligustrum japonicum 'Texanum'. Not sure about deer resistance though. You'll need to research.

Also one of the Pyracanthus. If you don't mind thorns.

Deer LOVE loquats (at least the leaves). Deer WILL nibble on Photinia if there is not much else green in your (or your neighbor's) Winter landscape. I purchased some Ligustrum japonicum 'Texanum' because have read that they are deer resistant but they are not in the ground yet, so not sure. Osmanthus 'Goshiki' (forgot the species name on it), is deer proof but not sure it is a fast grower.
Magnolia grandiflora is deer proof BUT, they DEER LOVE THEM during the rut and will mark them if they can get close (and they are much taller than your height requirement). 'English' Laurel and Bay Laurel are also highly resistant, as is Boxwood. My Holly (including; Nellie Stevens, Inkberry, Japanese), Fargesia bamboo, and rhododendrons are completely ignored. Butterfly bush too, which should be evergreen for you, (it is largely evergreen here). Others? Consider,Yuccas or Ornamental grasses too. These have worked for me, but not sure all are reliable in your area. Good luck!

I need this same thing except the ares I want to screen is full shade. I'm in zone 7a. Would enjoy some flowering of edible berry for birds.

Bayberry works in shade in my northern VA garden-well, not deep shade. It get some filtered sun part of the day. The one on the south side of the house is doing better (growing faster) than the one on the north side which actually gets a little more sun. Both are on our side of neighbors' fences. I planted them because they will get 10-12 feet tall and they are evergreen and native.

no plant.. EVER.. stops growing at some magical height ... most size estimates are at 10 years ... though i am not sure that general ruoles holds true in the shrub realm ....

to keep something at a preferred height ... you use REJUVENATION PRUNING... thru the years ...

or.. you just ignore it.. for a decade or two.. and then witch and moan ...

i am not familiar with growing things in bengal ... so i hesitate to offer suggestions ... if you are not there.. and want rather useful information.. i suggest you tell us where you are ... because.. e.g. ...some of the suggestions given wont grow in my z5 MI ...

BTW ...nothing is drought proof for a year or two after planting.. many.. if not most shrubs are such .... thereafter .... its called getting ESTABLISHED ....

ken

I have had great success with variegated privet. They grow large and bushy but can be kept under control. they are inexpensive and readily available. However, we don't have deer except in our freezer.