This button says Savannah on one side and something else on the other. It looks like the George State Seal Pillars on the front. Can anyone identify it? I'm in the midst of cleaning it.
Since it seems nobody else is willing to hazard a guess on your brass 3-piece Savannah Police button's age, I'll try. It appears to have what civil war button collectors call a "wide rim" (in comparison to the typical civil war period "narrow rim" on 3-piece buttons). The wide rim became popular a decade or so after the civil war, approximately 1870s/80s. There's even an "extra-wide" rim version. Because the words narrow, wide, and extra-wide are open to interpretation, here's a photo (below) showing New York State Militia 3-piece buttons with (from left to right) a wide, narrow, and extra-wide rim.
All of that being said... your photos of the still-encrusted button aren't quite clear enough for me to be 100%-certain that it has a wide rim. With the photo below, you can judge your button's rim size better than me.
Also, please try cleaning up the button's back and tell us any letters you can discern in the button's backmark. Well-focused closeup photos of the cleaned back might also help.
Interesting. I am slowly cleaning it, but will have a few much better pics on Wednesday evening when I get back from a business trip. The back should be legible by then.
I've got great news for you. Your Savannah Police button's backmark says "J.M.L. & W.H. Scovill / Waterbury" on the outer ring of lettering, and "Extra Superfine" on an inner ring of lettering. The Scovill firm was in business under that name from 1827 to 1840 (when its name changed to Scovills & Company). Therefore, your J.M.L. & W.H. Scovill 3-piece button dates from sometime in the 1830s up to 1840, because 3-piece buttons didn't exist until the 1830s.
You asked what is it worth. "Antique" historical Military buttons have the most dollar-value to collectors. Your button is not Military... it's a Police button. It was made about 25 years before the start of the civil war. A Confederate soldier may have used it to replace a lost CS military button on his uniform... but there's no way to prove that happened.
There are people who collect Police buttons, especially ones from the 1800s, and yours from the 1830s would be of high interest to those people. Also, it is in very good condition for an excavated button, which helps its value a lot. If you want to sell it, put it on Ebay, in the Antiques > Collectibles> Police > Buttons category (or whatever category is closest to that subject area).