Ok guys here goes, I haven't been able to find out much about it so far other than it seems very old and I love it lol.

It is a Top-Break but I don't see a CTG or Caliber on it but was loaded with REM UMC .38 S&W when I got it. It is stamped Smith & Wesson but the only writing on the gun is on the top of the barrel, there is nothing on the side at all clean nickel finish. No hammer and has a button to release the top break.

Basic info best I can tell:
Pearl or Ivory handle
Serial# 20283 (Butt of gun and on cylinder)
3 1/4" Barrel
Fixed Sights
3 Screw Frame
Does have a Strain Screw

On top of the barrel it reads (very small and difficult)
Smith & Wesson Springfield Mass USA PAT'D FEBY
20.77.Dec.18.77.May.11.80.Sept.11.83.Oct.2.83.TWO AUG.4.65

Any info would be much appreciated and Thank You all in advance.
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Looks like a 2nd Model Safety Hammerless too me. Unique in the barrel latch release it has on it. They were made from 1887 to 1890 serial numbers were from 5251 through 42483. This according to the Standard Catalog that most of us are using. Welcome to the forum. Do you intend to shoot it? There fun shooters but ammo can be a bit expensive. Kyle

Thanks for the welcome, not sure if I'm going to shoot it or not but I've considered it. When I got it it was with some old rounds, REM UMC .38 S&W lead. Pretty old doubt there safe enough to fire but I may go pick some up today.

Does anyone know what the numbers on top of it might mean by chance? Would those be patent dates?

Yes, those would be patent dates. If your markings are all very faint and your trigger is nickeled (hard to tell from the photos but it should be color case hardened) then your little pistol has been renickeled and somewhat devalued because of it.
This is the gun with many names: safety hammerless, lemon squeezer, or new departure. I have one and it is a neat little pistol. Many of them were carried by ladies or affluent men. They were easily concealed in a pocket by bankers and business men.
I hear original pearl grips are quite valuable, too.

The marking and dates are pretty easy to read not blurry just small and a bit hard to see for me. It doesn't appear refinished, and I'm hoping the grips are original.

Providing that it has not been refinished and has original handles any idea of the estimated value on this piece?

I don't believe it has been refinished from the look of some of the pins. It's really hard to tell from the pictures. The grips may be real mother-of-pearl, but I doubt they are factory originals. IIRC, S&W put medallions in their pearl and ivory grips. They should still be quite valuable if they aren't chipped and cracked.

__________________
Guy
SWHF #474 SWCA LM#2629

After market pearl grips do have some value but in this case they just contribute to the condition of the gun which appears excellent. The unkonown factor is whether it has been refinished. The trigger looks to have been plated which is a sure giveaway - it should be case hardened. If not refinished it should go for $400-$450.
Nice gun.

Stan

Finally took it out to shoot some yesterday, happy to update that it performed without any flaws, shoots a bit high and hardly any recoil, but overall a nice little pistol.