HoleDiver, thank you for making and posting the requested "better" photos of your button's front and back.
In the previous photos, I thought one of the symbols on its "quartered" emblem was a crescent-moon-with-star. Your new photo shows that's not what it is. I still can't make out any of the other three symbols. They may be too corroded to ever identify. What makes the first symbol visible is the goldplating which still surrounds it because the background is recessed, and thus the goldplating got protected from being rubbed off as the button was used (perhaps every day). My point is, the goldplating in the recesses around the other symbols should also still be present. You might want to try cleaning the button's front a bit more, by briefly soaking it in lemon juice or ammonia or Tob Job cleaner, then dip the tip of a toothbrush in the cleaner and gently scrub the button's front, especially around the emblems. (Then rinse the button off quite thoroughly.)
Meanwhile, all I can tell you is that the evidence indicates your button is a civilian "Fashion" coat or jacket or sweater button, from the 1840s through MAYBE as late as the very-early 20th-Century. Reasons:
1: It seems to have genuine gold plating -- not cheap "gold finish" like nearly all 20th-Century "Fashion" buttons. Actual gold plating of course makes the button cost a lot more.
2: Although it has an iron back, it has a loop, instead of having an iron/steel "self-shank" back -- which is much cheaper to manufacture than a back with a loop. "Self-shank" backs became common in the early 20th-Century, as a costcutting method, and have remained the standard back for inexpensively-produced buttons ever since.
3: Related to cost-of-manufacure... the loop is brass wire, which costs significantly more than iron wire.
So, putting together all those factors relating to cost and quality and construction-type, in my opinion your button is from the mid to late 1800s. Button-collectors call that time-period the "Golden Age" age of buttons, because that is when the most-ornate, well-constructed, actual-goldplated metal buttons were the common standard instead of the rare exception in the buttonmaking industry.