The "Secret Service Special" revolvers were sold by the Fred Biffar Co., a Chicago based firm, in the early 1900's. They were actually subcontracted out to several different manufacturers. Meridian made early versions. Iver Johnson made a lot. Hopkins and Allen and H&R all had contracts as well. The Iver J's were probably the best made. They had frame mounted firing pins with a hammer block safety. The front of the trigger guard was held in place by an internal screw. The H&A and H&R models both had hammer mounted firing pins as well as trigger guard pins fore and aft. Hard to tell by your picture but it looks like a pin is holding the front of the trigger guard in place. Yours looks like the Hopkins & Allen product. Is the firing pin on the hammer?
I have several old S&W, IJ's and H&R top breaks and have shot 32 S&W factory ammo out of the ones in better shape. While the factory loads are kept mild, the 32 S&W being a very underpowered cartridge to begin with, I prefer to shoot reloads using about 1.2 g of Trail Boss. They are fun to shoot but you should have a smith look at it first. The difference in quality and workmanship between the S&W top breaks and all others is remarkable and accounts for their double or more sale price at the time.
BTW, welcome to the forum!